Control of chaos in Hamiltonian systems

汉密尔顿原理The Hamiltonian principle, also known as Hamilton's principle, is a fundamental principle in classical mechanics. It states that the dynamics of a physical system are determined by a single function, known as the Hamiltonian. This principle was formulated by Sir William Rowan Hamilton in 1834 and is a powerful tool for understanding the behavior of a wide range of physical systems.汉密尔顿原理，也称为汉密尔顿原则，是古典力学中的基本原理。

它表明物理系统的动力学是由一个称为汉密尔顿量的单个函数所决定的。

这一原理是由威廉·罗恩·汉密尔顿爵士于1834年提出的，是理解各种物理系统行为的有力工具。

One of the key insights of the Hamiltonian principle is that it provides a more general formulation of the laws of motion than the standard Newtonian approach. While Newton's laws are suitable for describing the motion of simple, low-energy systems, the Hamiltonian approach can be applied to more complex systems, including those involving relativistic effects and quantum mechanics.汉密尔顿原理的一个关键见解是，它提供了比标准牛顿方法更一般的运动定律公式。

对混沌自适应控制的控制强度的讨论之二何花;赵泓【期刊名称】《计算机工程与设计》【年(卷),期】2001(022)002【摘要】文中对文献[1]提出的混沌自适应控制方法中给出的控制强度取值范围的计算方法作出了重要修改，指出了上文忽略的与控制矩阵的复数本征值λ±对应的控制强度，对离散系统只要满足｜λ±｜＜1亦可控制混沌，且更有效。

其次指出对连续性系统仅考虑文献[1]给出的条件是不够的，控制强度还要满足λ±值的实部小于零，即微分方程的李雅普诺夫渐近稳定条件才能有效控制混沌。

%This paper make important correction for reference [1]. We point out it is more effective that the control stiffness is correspending to complex eigenvalue of the matrix introduced by linearizing the dynamic system, it can also control chaos when ｜λ±｜＜1 for discrete system. We point out it is ont enough for control chaos of continuous system that only consider the condition proved by reference [1], the control stiffness should accord with the condition of Re (｜λ±｜) ＜0.【总页数】4页(P70-73)【作者】何花;赵泓【作者单位】首都师范大学计算机系,物理系,;首都师范大学计算机系,物理系,【正文语种】中文【中图分类】O545;TP273.2【相关文献】1.电弧喷涂控制系统研究之二——系统控制参数优化及自适应控制设计 [J], 李鹤歧;李春旭;陈爱军2.超混沌Lorenz系统与超混沌Rossler系统的自适应控制同步 [J], 蒋楠3.基于自适应控制的八个混沌系统的多级组合同步 [J], 孙军伟; 李楠; 王延峰4.对混沌自适应控制方法的控制强度的讨论 [J], 赵泓;何花;沈京玲5.耦合时空混沌的模糊混沌神经网络鲁棒自适应控制 [J], 窦春霞;李鑫滨;袁石文因版权原因，仅展示原文概要，查看原文内容请购买。

一类混沌系统的状态量化反馈镇定控制器设计翟因虎;王银河;范永青【摘要】This paper investigates the asymptotical stabilization via state feedback for a class of chaotic systems with a quantizer connected on the input channel.The nonlinear terms in the dynamic equation of the chaotic system are represented as the homogeneous functions with arbitrary known orders.The quan-tizer has one adjustable time-varying parameter with the updated law to be designed, and thus it can quantify adaptively online the state variables of the chaotic systems according to control scheme.With the help of the updated law and adaptive law of estimated boundary error of quantization, the nonlinear adap-tive controller is proposed in this paper to ensure the chaotic system to be stabilized asymptotically in the presence of the quantizer.Finally, some simulation examples are utilized to demonstrate the validity of the results in this paper.%用状态反馈法对含量化器的一类混沌系统的渐进镇定进行了研究。

工商管理学院牛东晓，男，日生Prepared on 22 November 2020乞建勋，男，1946年10月生，汉族，现为华北电力大学工商管理学院教授，博士生导师。

乞建勋教授是我国技术经济预测与决策领域的专家，长期以来一直从数学的角度研究现代管理的新方法，尤其在网络计划管理与优化理论的研究中取得了突破性重大进展。

推导出了"机动时间定理"、"路长定理"、"非特征路线定理"等优化的基本定理，并利用这些定理解决了最低成本加快方法中的最大有效压缩量和群截面的求法，解决了各阶次关键路线的求法等一系列的网络计划优化的悬而未决的问题。

尤其是在近二三十年被国际一致公认的疑难问题--工序顺序排序优化问题上取得了重大突破，解决了常见的一些应用最广的特殊情况下的顺序优化问题，创造出了一套独特方法，为彻底解决该难题奠定了基础。

在国内外权威刊物上发表网络计划论文六十多篇，并由科学出版社出版了网络计划优化领域中第一部学术专着《网络计划优化新理论与技术经济决策》，在该领域的研究中达到国际先进水平。

兼任全国系统动力学学会理事、全国项目管理委员会委员、全国价值工程协会理事、《华北电力大学学报》编委、《价值工程》编委。

先后承担及主持的纵向、横向科研课题十余项。

其中一项为国家电力公司重大科研项目，一项获部级科技进步奖。

在2001－2006年间，电力管理与优化决策研究所承担了3项纵向课题：国家自然科学基金重大项目（），国家自然科学基金项目（），国家教育部博士点基金项目（008）；横向课题17项。

其中《电厂大修的网络计划优化新理论及其软件开发》获得电力科学技术三等奖。

主要研究方向：优化理论与技术经济决策、技术经济评价理论与应用、电力经济管理。

牛东晓，男，1962年10月15日生，汉族，安徽宿县人，现任华北电力大学工商管理学院院长。

牛东晓教授是技术经济预测与决策领域的专家，致力于电力与经济系统中的预测与决策问题的研究，同时也开展电力工程建设项目技术经济评价的研究，曾获得中国电力科学技术二等奖、中国电力科学技术三等奖、国家教委科技进步三等奖、国家电力公司首届青年科技创新奖和河北省第三届青年科技奖等共6项省部级科技成果奖。

混沌控制：方法与应用B.R.Andrievskii和A.L.Fradkov俄罗斯科学院机械科学问题研究所，俄罗斯圣彼得堡，接收于2003年11月04日。

摘要：混沌的控制是最近十年被密集研究的一项课题，对它的的研究主要集中在应用方面，也即考虑其在不同的科学领域，如力学(控制的钟摆，梁、板、摩擦)，物理(等离子体控制的动荡，激光，混沌，和传播的偶极子域)，化学、生物学、生态学、经济学、医学、以及其他工程学如机械系统(控制vibroformers、微悬臂起重机、船)，宇宙飞船，电气和电子系统，通信系统，信息系统，化学和加工工业中（信息流处理和自由流动物质的处理）的重要应用。

关键词：混沌，控制理论，科学应用，抑制混沌，工业应用。

1.引言在确定性混沌的概念渗透到科学文献的第一年，混沌的行为就被认为是一个奇特的现象，它或许只会出现在一个在实践中永远不会遇到的复杂数学运算中。

但是，后来，混沌运动现象被发现存在于许多系统力学、通信、激光和无线电物理(10、12、16、18、19)，化学和生物化学[46]、[55]生物学，经济学(124，124)，和药品领域。

在1997年和2002年之间有超过300篇发表在同行评议期刊的论文致力于研究混沌控制方法在多种情况下的应用。

在科学和技术领域如混沌流线物理过程，激光物理和光学、等离子体物理、分子和量子物理、力学、化学和电化学、生物学和生态学、经济学和财务、医学、机械工程、电气工程和化工、交通控制、通信与信息系统，混沌控制方法的问题一直都被积极探讨。

混沌控制在工程应用领域的实践证明了混沌的价值和混沌系统的控制方法在特定实际问题中的作用，也起码证明了混沌控制应用的可行性。

但是，混沌在科学领域的应用(在物理、化学或生物学)，主要是朝向发现物理(化学、生物)系统行为中的新属性和规律的控制理论和方法方面发展，而不是特定的应用。

他们经常利用简单的模型描述被研究的系统。

科学应用2.1.机械系统混沌控制应用钟摆，梁和盘中的混沌控制。

哈密顿拉格朗日多体系统动力学（中英文实用版）Title: Hamilton and Lagrange Multibody System DynamicsHamilton"s mechanics and Lagrange"s equations are two essential frameworks in the field of multibody system dynamics.They provide a mathematical description of the motion of systems composed of multiple interacting particles or bodies.Hamilton"s mechanics, formulated by William Rowan Hamilton in the early 19th century, is based on the principle of least action.It provides a comprehensive framework for describing the dynamics of systems with a wide range of complexity, from simple mechanical systems to celestial mechanics and quantum mechanics.In Hamilton"s mechanics, the equations of motion are derived from the action principle, which states that the actual path of a system is the one that minimizes the action, a functional that depends on the configuration and time evolution of the system.In Chinese, Hamilton mechanics, formulated by William Rowan Hamilton in the early 19th century, is based on the principle of least action.It provides a comprehensive framework for describing the dynamics of systems with a wide range of complexity, from simple mechanical systems to celestial mechanics and quantum mechanics.In Hamilton"s mechanics, the equations of motion are derived from theaction principle, which states that the actual path of a system is the one that minimizes the action, a functional that depends on the configuration and time evolution of the system.Lagrange"s equations, on the other hand, were formulated by Joseph-Louis Lagrange in the mid-18th century.They provide an alternative approach to the study of dynamic systems, focusing on the conservation of grange"s equations are derived from the principle of virtual work, which states that the actual motion of a system is the one that minimizes the potential energy of the system.In Lagrange"s framework, the equations of motion are expressed in terms of generalized coordinates and their derivatives, which represent the configuration and time evolution of the system.In contrast to Hamilton"s mechanics, Lagrange"s equations focus on the conservation of energy.They were formulated by Joseph-Louis Lagrange in the mid-18th century.In Lagrange"s framework, the equations of motion are expressed in terms of generalized coordinates and their derivatives, which represent the configuration and time evolution of the system.The principle of virtual work underlies Lagrange"s equations, stating that the actual motion of a system is the one that minimizes the potential energy of the system.Both Hamilton"s and Lagrange"s frameworks are widely used in the study of multibody system dynamics.They provide powerful tools foranalyzing the motion of complex systems, such as robotic arms, vehicles, and biological organisms.By employing these frameworks, researchers and engineers can accurately predict the behavior of these systems under various conditions and design optimal control strategies for their operation.In summary, Hamilton"s and Lagrange"s mechanics are two complementary frameworks that play a crucial role in the analysis of multibody system dynamics.They provide a mathematical description of the motion of systems composed of multiple interacting particles or bodies, allowing for the study and optimization of complex dynamic systems.。

华中师范大学物理学院物理学专业英语仅供内部学习参考！2014一、课程的任务和教学目的通过学习《物理学专业英语》，学生将掌握物理学领域使用频率较高的专业词汇和表达方法，进而具备基本的阅读理解物理学专业文献的能力。

通过分析《物理学专业英语》课程教材中的范文，学生还将从英语角度理解物理学中个学科的研究内容和主要思想，提高学生的专业英语能力和了解物理学研究前沿的能力。

培养专业英语阅读能力，了解科技英语的特点，提高专业外语的阅读质量和阅读速度；掌握一定量的本专业英文词汇，基本达到能够独立完成一般性本专业外文资料的阅读；达到一定的笔译水平。

要求译文通顺、准确和专业化。

要求译文通顺、准确和专业化。

二、课程内容课程内容包括以下章节：物理学、经典力学、热力学、电磁学、光学、原子物理、统计力学、量子力学和狭义相对论三、基本要求1.充分利用课内时间保证充足的阅读量（约1200~1500词/学时），要求正确理解原文。

2.泛读适量课外相关英文读物，要求基本理解原文主要内容。

3.掌握基本专业词汇（不少于200词）。

4.应具有流利阅读、翻译及赏析专业英语文献，并能简单地进行写作的能力。

四、参考书目录1 Physics 物理学 (1)Introduction to physics (1)Classical and modern physics (2)Research fields (4)V ocabulary (7)2 Classical mechanics 经典力学 (10)Introduction (10)Description of classical mechanics (10)Momentum and collisions (14)Angular momentum (15)V ocabulary (16)3 Thermodynamics 热力学 (18)Introduction (18)Laws of thermodynamics (21)System models (22)Thermodynamic processes (27)Scope of thermodynamics (29)V ocabulary (30)4 Electromagnetism 电磁学 (33)Introduction (33)Electrostatics (33)Magnetostatics (35)Electromagnetic induction (40)V ocabulary (43)5 Optics 光学 (45)Introduction (45)Geometrical optics (45)Physical optics (47)Polarization (50)V ocabulary (51)6 Atomic physics 原子物理 (52)Introduction (52)Electronic configuration (52)Excitation and ionization (56)V ocabulary (59)7 Statistical mechanics 统计力学 (60)Overview (60)Fundamentals (60)Statistical ensembles (63)V ocabulary (65)8 Quantum mechanics 量子力学 (67)Introduction (67)Mathematical formulations (68)Quantization (71)Wave-particle duality (72)Quantum entanglement (75)V ocabulary (77)9 Special relativity 狭义相对论 (79)Introduction (79)Relativity of simultaneity (80)Lorentz transformations (80)Time dilation and length contraction (81)Mass-energy equivalence (82)Relativistic energy-momentum relation (86)V ocabulary (89)正文标记说明：蓝色Arial字体（例如energy）：已知的专业词汇蓝色Arial字体加下划线（例如electromagnetism）：新学的专业词汇黑色Times New Roman字体加下划线（例如postulate）：新学的普通词汇1 Physics 物理学1 Physics 物理学Introduction to physicsPhysics is a part of natural philosophy and a natural science that involves the study of matter and its motion through space and time, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic disciplines, perhaps the oldest through its inclusion of astronomy. Over the last two millennia, physics was a part of natural philosophy along with chemistry, certain branches of mathematics, and biology, but during the Scientific Revolution in the 17th century, the natural sciences emerged as unique research programs in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry,and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms of other sciences, while opening new avenues of research in areas such as mathematics and philosophy.Physics also makes significant contributions through advances in new technologies that arise from theoretical breakthroughs. For example, advances in the understanding of electromagnetism or nuclear physics led directly to the development of new products which have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.Core theoriesThough physics deals with a wide variety of systems, certain theories are used by all physicists. Each of these theories were experimentally tested numerous times and found correct as an approximation of nature (within a certain domain of validity).For instance, the theory of classical mechanics accurately describes the motion of objects, provided they are much larger than atoms and moving at much less than the speed of light. These theories continue to be areas of active research, and a remarkable aspect of classical mechanics known as chaos was discovered in the 20th century, three centuries after the original formulation of classical mechanics by Isaac Newton (1642–1727) 【艾萨克·牛顿】.University PhysicsThese central theories are important tools for research into more specialized topics, and any physicist, regardless of his or her specialization, is expected to be literate in them. These include classical mechanics, quantum mechanics, thermodynamics and statistical mechanics, electromagnetism, and special relativity.Classical and modern physicsClassical mechanicsClassical physics includes the traditional branches and topics that were recognized and well-developed before the beginning of the 20th century—classical mechanics, acoustics, optics, thermodynamics, and electromagnetism.Classical mechanics is concerned with bodies acted on by forces and bodies in motion and may be divided into statics (study of the forces on a body or bodies at rest), kinematics (study of motion without regard to its causes), and dynamics (study of motion and the forces that affect it); mechanics may also be divided into solid mechanics and fluid mechanics (known together as continuum mechanics), the latter including such branches as hydrostatics, hydrodynamics, aerodynamics, and pneumatics.Acoustics is the study of how sound is produced, controlled, transmitted and received. Important modern branches of acoustics include ultrasonics, the study of sound waves of very high frequency beyond the range of human hearing; bioacoustics the physics of animal calls and hearing, and electroacoustics, the manipulation of audible sound waves using electronics.Optics, the study of light, is concerned not only with visible light but also with infrared and ultraviolet radiation, which exhibit all of the phenomena of visible light except visibility, e.g., reflection, refraction, interference, diffraction, dispersion, and polarization of light.Heat is a form of energy, the internal energy possessed by the particles of which a substance is composed; thermodynamics deals with the relationships between heat and other forms of energy.Electricity and magnetism have been studied as a single branch of physics since the intimate connection between them was discovered in the early 19th century; an electric current gives rise to a magnetic field and a changing magnetic field induces an electric current. Electrostatics deals with electric charges at rest, electrodynamics with moving charges, and magnetostatics with magnetic poles at rest.Modern PhysicsClassical physics is generally concerned with matter and energy on the normal scale of1 Physics 物理学observation, while much of modern physics is concerned with the behavior of matter and energy under extreme conditions or on the very large or very small scale.For example, atomic and nuclear physics studies matter on the smallest scale at which chemical elements can be identified.The physics of elementary particles is on an even smaller scale, as it is concerned with the most basic units of matter; this branch of physics is also known as high-energy physics because of the extremely high energies necessary to produce many types of particles in large particle accelerators. On this scale, ordinary, commonsense notions of space, time, matter, and energy are no longer valid.The two chief theories of modern physics present a different picture of the concepts of space, time, and matter from that presented by classical physics.Quantum theory is concerned with the discrete, rather than continuous, nature of many phenomena at the atomic and subatomic level, and with the complementary aspects of particles and waves in the description of such phenomena.The theory of relativity is concerned with the description of phenomena that take place in a frame of reference that is in motion with respect to an observer; the special theory of relativity is concerned with relative uniform motion in a straight line and the general theory of relativity with accelerated motion and its connection with gravitation.Both quantum theory and the theory of relativity find applications in all areas of modern physics.Difference between classical and modern physicsWhile physics aims to discover universal laws, its theories lie in explicit domains of applicability. Loosely speaking, the laws of classical physics accurately describe systems whose important length scales are greater than the atomic scale and whose motions are much slower than the speed of light. Outside of this domain, observations do not match their predictions.Albert Einstein【阿尔伯特·爱因斯坦】contributed the framework of special relativity, which replaced notions of absolute time and space with space-time and allowed an accurate description of systems whose components have speeds approaching the speed of light.Max Planck【普朗克】, Erwin Schrödinger【薛定谔】, and others introduced quantum mechanics, a probabilistic notion of particles and interactions that allowed an accurate description of atomic and subatomic scales.Later, quantum field theory unified quantum mechanics and special relativity.General relativity allowed for a dynamical, curved space-time, with which highly massiveUniversity Physicssystems and the large-scale structure of the universe can be well-described. General relativity has not yet been unified with the other fundamental descriptions; several candidate theories of quantum gravity are being developed.Research fieldsContemporary research in physics can be broadly divided into condensed matter physics; atomic, molecular, and optical physics; particle physics; astrophysics; geophysics and biophysics. Some physics departments also support research in Physics education.Since the 20th century, the individual fields of physics have become increasingly specialized, and today most physicists work in a single field for their entire careers. "Universalists" such as Albert Einstein (1879–1955) and Lev Landau (1908–1968)【列夫·朗道】, who worked in multiple fields of physics, are now very rare.Condensed matter physicsCondensed matter physics is the field of physics that deals with the macroscopic physical properties of matter. In particular, it is concerned with the "condensed" phases that appear whenever the number of particles in a system is extremely large and the interactions between them are strong.The most familiar examples of condensed phases are solids and liquids, which arise from the bonding by way of the electromagnetic force between atoms. More exotic condensed phases include the super-fluid and the Bose–Einstein condensate found in certain atomic systems at very low temperature, the superconducting phase exhibited by conduction electrons in certain materials,and the ferromagnetic and antiferromagnetic phases of spins on atomic lattices.Condensed matter physics is by far the largest field of contemporary physics.Historically, condensed matter physics grew out of solid-state physics, which is now considered one of its main subfields. The term condensed matter physics was apparently coined by Philip Anderson when he renamed his research group—previously solid-state theory—in 1967. In 1978, the Division of Solid State Physics of the American Physical Society was renamed as the Division of Condensed Matter Physics.Condensed matter physics has a large overlap with chemistry, materials science, nanotechnology and engineering.Atomic, molecular and optical physicsAtomic, molecular, and optical physics (AMO) is the study of matter–matter and light–matter interactions on the scale of single atoms and molecules.1 Physics 物理学The three areas are grouped together because of their interrelationships, the similarity of methods used, and the commonality of the energy scales that are relevant. All three areas include both classical, semi-classical and quantum treatments; they can treat their subject from a microscopic view (in contrast to a macroscopic view).Atomic physics studies the electron shells of atoms. Current research focuses on activities in quantum control, cooling and trapping of atoms and ions, low-temperature collision dynamics and the effects of electron correlation on structure and dynamics. Atomic physics is influenced by the nucleus (see, e.g., hyperfine splitting), but intra-nuclear phenomena such as fission and fusion are considered part of high-energy physics.Molecular physics focuses on multi-atomic structures and their internal and external interactions with matter and light.Optical physics is distinct from optics in that it tends to focus not on the control of classical light fields by macroscopic objects, but on the fundamental properties of optical fields and their interactions with matter in the microscopic realm.High-energy physics (particle physics) and nuclear physicsParticle physics is the study of the elementary constituents of matter and energy, and the interactions between them.In addition, particle physicists design and develop the high energy accelerators,detectors, and computer programs necessary for this research. The field is also called "high-energy physics" because many elementary particles do not occur naturally, but are created only during high-energy collisions of other particles.Currently, the interactions of elementary particles and fields are described by the Standard Model.●The model accounts for the 12 known particles of matter (quarks and leptons) thatinteract via the strong, weak, and electromagnetic fundamental forces.●Dynamics are described in terms of matter particles exchanging gauge bosons (gluons,W and Z bosons, and photons, respectively).●The Standard Model also predicts a particle known as the Higgs boson. In July 2012CERN, the European laboratory for particle physics, announced the detection of a particle consistent with the Higgs boson.Nuclear Physics is the field of physics that studies the constituents and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation and nuclear weapons technology, but the research has provided application in many fields, including those in nuclear medicine and magnetic resonance imaging, ion implantation in materials engineering, and radiocarbon dating in geology and archaeology.University PhysicsAstrophysics and Physical CosmologyAstrophysics and astronomy are the application of the theories and methods of physics to the study of stellar structure, stellar evolution, the origin of the solar system, and related problems of cosmology. Because astrophysics is a broad subject, astrophysicists typically apply many disciplines of physics, including mechanics, electromagnetism, statistical mechanics, thermodynamics, quantum mechanics, relativity, nuclear and particle physics, and atomic and molecular physics.The discovery by Karl Jansky in 1931 that radio signals were emitted by celestial bodies initiated the science of radio astronomy. Most recently, the frontiers of astronomy have been expanded by space exploration. Perturbations and interference from the earth's atmosphere make space-based observations necessary for infrared, ultraviolet, gamma-ray, and X-ray astronomy.Physical cosmology is the study of the formation and evolution of the universe on its largest scales. Albert Einstein's theory of relativity plays a central role in all modern cosmological theories. In the early 20th century, Hubble's discovery that the universe was expanding, as shown by the Hubble diagram, prompted rival explanations known as the steady state universe and the Big Bang.The Big Bang was confirmed by the success of Big Bang nucleo-synthesis and the discovery of the cosmic microwave background in 1964. The Big Bang model rests on two theoretical pillars: Albert Einstein's general relativity and the cosmological principle (On a sufficiently large scale, the properties of the Universe are the same for all observers). Cosmologists have recently established the ΛCDM model (the standard model of Big Bang cosmology) of the evolution of the universe, which includes cosmic inflation, dark energy and dark matter.Current research frontiersIn condensed matter physics, an important unsolved theoretical problem is that of high-temperature superconductivity. Many condensed matter experiments are aiming to fabricate workable spintronics and quantum computers.In particle physics, the first pieces of experimental evidence for physics beyond the Standard Model have begun to appear. Foremost among these are indications that neutrinos have non-zero mass. These experimental results appear to have solved the long-standing solar neutrino problem, and the physics of massive neutrinos remains an area of active theoretical and experimental research. Particle accelerators have begun probing energy scales in the TeV range, in which experimentalists are hoping to find evidence for the super-symmetric particles, after discovery of the Higgs boson.Theoretical attempts to unify quantum mechanics and general relativity into a single theory1 Physics 物理学of quantum gravity, a program ongoing for over half a century, have not yet been decisively resolved. The current leading candidates are M-theory, superstring theory and loop quantum gravity.Many astronomical and cosmological phenomena have yet to be satisfactorily explained, including the existence of ultra-high energy cosmic rays, the baryon asymmetry, the acceleration of the universe and the anomalous rotation rates of galaxies.Although much progress has been made in high-energy, quantum, and astronomical physics, many everyday phenomena involving complexity, chaos, or turbulence are still poorly understood. Complex problems that seem like they could be solved by a clever application of dynamics and mechanics remain unsolved; examples include the formation of sand-piles, nodes in trickling water, the shape of water droplets, mechanisms of surface tension catastrophes, and self-sorting in shaken heterogeneous collections.These complex phenomena have received growing attention since the 1970s for several reasons, including the availability of modern mathematical methods and computers, which enabled complex systems to be modeled in new ways. Complex physics has become part of increasingly interdisciplinary research, as exemplified by the study of turbulence in aerodynamics and the observation of pattern formation in biological systems.Vocabulary★natural science 自然科学academic disciplines 学科astronomy 天文学in their own right 凭他们本身的实力intersects相交，交叉interdisciplinary交叉学科的，跨学科的★quantum 量子的theoretical breakthroughs 理论突破★electromagnetism 电磁学dramatically显著地★thermodynamics热力学★calculus微积分validity★classical mechanics 经典力学chaos 混沌literate 学者★quantum mechanics量子力学★thermodynamics and statistical mechanics热力学与统计物理★special relativity狭义相对论is concerned with 关注，讨论，考虑acoustics 声学★optics 光学statics静力学at rest 静息kinematics运动学★dynamics动力学ultrasonics超声学manipulation 操作，处理，使用University Physicsinfrared红外ultraviolet紫外radiation辐射reflection 反射refraction 折射★interference 干涉★diffraction 衍射dispersion散射★polarization 极化，偏振internal energy 内能Electricity电性Magnetism 磁性intimate 亲密的induces 诱导，感应scale尺度★elementary particles基本粒子★high-energy physics 高能物理particle accelerators 粒子加速器valid 有效的，正当的★discrete离散的continuous 连续的complementary 互补的★frame of reference 参照系★the special theory of relativity 狭义相对论★general theory of relativity 广义相对论gravitation 重力，万有引力explicit 详细的，清楚的★quantum field theory 量子场论★condensed matter physics凝聚态物理astrophysics天体物理geophysics地球物理Universalist博学多才者★Macroscopic宏观Exotic奇异的★Superconducting 超导Ferromagnetic铁磁质Antiferromagnetic 反铁磁质★Spin自旋Lattice 晶格，点阵，网格★Society社会，学会★microscopic微观的hyperfine splitting超精细分裂fission分裂，裂变fusion熔合，聚变constituents成分，组分accelerators加速器detectors 检测器★quarks夸克lepton 轻子gauge bosons规范玻色子gluons胶子★Higgs boson希格斯玻色子CERN欧洲核子研究中心★Magnetic Resonance Imaging磁共振成像，核磁共振ion implantation 离子注入radiocarbon dating放射性碳年代测定法geology地质学archaeology考古学stellar 恒星cosmology宇宙论celestial bodies 天体Hubble diagram 哈勃图Rival竞争的★Big Bang大爆炸nucleo-synthesis核聚合，核合成pillar支柱cosmological principle宇宙学原理ΛCDM modelΛ-冷暗物质模型cosmic inflation宇宙膨胀1 Physics 物理学fabricate制造，建造spintronics自旋电子元件，自旋电子学★neutrinos 中微子superstring 超弦baryon重子turbulence湍流，扰动，骚动catastrophes突变，灾变，灾难heterogeneous collections异质性集合pattern formation模式形成University Physics2 Classical mechanics 经典力学IntroductionIn physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces. The study of the motion of bodies is an ancient one, making classical mechanics one of the oldest and largest subjects in science, engineering and technology.Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. Besides this, many specializations within the subject deal with gases, liquids, solids, and other specific sub-topics.Classical mechanics provides extremely accurate results as long as the domain of study is restricted to large objects and the speeds involved do not approach the speed of light. When the objects being dealt with become sufficiently small, it becomes necessary to introduce the other major sub-field of mechanics, quantum mechanics, which reconciles the macroscopic laws of physics with the atomic nature of matter and handles the wave–particle duality of atoms and molecules. In the case of high velocity objects approaching the speed of light, classical mechanics is enhanced by special relativity. General relativity unifies special relativity with Newton's law of universal gravitation, allowing physicists to handle gravitation at a deeper level.The initial stage in the development of classical mechanics is often referred to as Newtonian mechanics, and is associated with the physical concepts employed by and the mathematical methods invented by Newton himself, in parallel with Leibniz【莱布尼兹】, and others.Later, more abstract and general methods were developed, leading to reformulations of classical mechanics known as Lagrangian mechanics and Hamiltonian mechanics. These advances were largely made in the 18th and 19th centuries, and they extend substantially beyond Newton's work, particularly through their use of analytical mechanics. Ultimately, the mathematics developed for these were central to the creation of quantum mechanics.Description of classical mechanicsThe following introduces the basic concepts of classical mechanics. For simplicity, it often2 Classical mechanics 经典力学models real-world objects as point particles, objects with negligible size. The motion of a point particle is characterized by a small number of parameters: its position, mass, and the forces applied to it.In reality, the kind of objects that classical mechanics can describe always have a non-zero size. (The physics of very small particles, such as the electron, is more accurately described by quantum mechanics). Objects with non-zero size have more complicated behavior than hypothetical point particles, because of the additional degrees of freedom—for example, a baseball can spin while it is moving. However, the results for point particles can be used to study such objects by treating them as composite objects, made up of a large number of interacting point particles. The center of mass of a composite object behaves like a point particle.Classical mechanics uses common-sense notions of how matter and forces exist and interact. It assumes that matter and energy have definite, knowable attributes such as where an object is in space and its speed. It also assumes that objects may be directly influenced only by their immediate surroundings, known as the principle of locality.In quantum mechanics objects may have unknowable position or velocity, or instantaneously interact with other objects at a distance.Position and its derivativesThe position of a point particle is defined with respect to an arbitrary fixed reference point, O, in space, usually accompanied by a coordinate system, with the reference point located at the origin of the coordinate system. It is defined as the vector r from O to the particle.In general, the point particle need not be stationary relative to O, so r is a function of t, the time elapsed since an arbitrary initial time.In pre-Einstein relativity (known as Galilean relativity), time is considered an absolute, i.e., the time interval between any given pair of events is the same for all observers. In addition to relying on absolute time, classical mechanics assumes Euclidean geometry for the structure of space.Velocity and speedThe velocity, or the rate of change of position with time, is defined as the derivative of the position with respect to time. In classical mechanics, velocities are directly additive and subtractive as vector quantities; they must be dealt with using vector analysis.When both objects are moving in the same direction, the difference can be given in terms of speed only by ignoring direction.University PhysicsAccelerationThe acceleration , or rate of change of velocity, is the derivative of the velocity with respect to time (the second derivative of the position with respect to time).Acceleration can arise from a change with time of the magnitude of the velocity or of the direction of the velocity or both . If only the magnitude v of the velocity decreases, this is sometimes referred to as deceleration , but generally any change in the velocity with time, including deceleration, is simply referred to as acceleration.Inertial frames of referenceWhile the position and velocity and acceleration of a particle can be referred to any observer in any state of motion, classical mechanics assumes the existence of a special family of reference frames in terms of which the mechanical laws of nature take a comparatively simple form. These special reference frames are called inertial frames .An inertial frame is such that when an object without any force interactions (an idealized situation) is viewed from it, it appears either to be at rest or in a state of uniform motion in a straight line. This is the fundamental definition of an inertial frame. They are characterized by the requirement that all forces entering the observer's physical laws originate in identifiable sources (charges, gravitational bodies, and so forth).A non-inertial reference frame is one accelerating with respect to an inertial one, and in such a non-inertial frame a particle is subject to acceleration by fictitious forces that enter the equations of motion solely as a result of its accelerated motion, and do not originate in identifiable sources. These fictitious forces are in addition to the real forces recognized in an inertial frame.A key concept of inertial frames is the method for identifying them. For practical purposes, reference frames that are un-accelerated with respect to the distant stars are regarded as good approximations to inertial frames.Forces; Newton's second lawNewton was the first to mathematically express the relationship between force and momentum . Some physicists interpret Newton's second law of motion as a definition of force and mass, while others consider it a fundamental postulate, a law of nature. Either interpretation has the same mathematical consequences, historically known as "Newton's Second Law":a m t v m t p F ===d )(d d dThe quantity m v is called the (canonical ) momentum . The net force on a particle is thus equal to rate of change of momentum of the particle with time.So long as the force acting on a particle is known, Newton's second law is sufficient to。

一种四维混沌系统的逆最优控制第27卷第3期2006年3月东北大学(自然科学版)JournalofNortheasternUniversity(NaturalScience)V o1.27.No.3Mar.2006文章编号:1005—3026(2006)03—0248—04一种四维混沌系统的逆最优控制谢英慧,张化光(东北大学信息科学与工程学院,辽宁沈阳110004)摘要:采用逆最优控制方法为一种四维混沌系统设计了一个线性状态反馈控制器.基于Lyapunov稳定性理论,证明了所设计的控制器能够使受控系统全局渐近稳定到系统的零平衡点,并且使所提出的目标泛函取得极小值.两组数值仿真均表明,所设计的控制器是实用有效,易于实现,并且具有很好的鲁棒性.在不同的初始条件下,所设计的控制器可以将受控四维混沌系统的混沌轨道很快控制到系统的零平衡点.关键词:四维混沌系统;逆最优控制;Lyapunov稳定性理论;全局渐近稳定;目标泛函中图分类号:O193文献标识码:A目前,国内外学者已提出许多不同的混沌控制方法,如反馈控制,自适应控制,延迟反馈控制,最优控制和模糊控制等【卜.其中最优控制是一种在系统控制中应用最为广泛的手段,并且问题最后都归结为求解Hamilton.Jacobi.Bellman偏微分方程(以下简称rUB方程).实际上,在许多情况下,rUB方程的解是不存在或不惟一的.因此,求解HJB方程是获得非线性系统最优控制的主要障碍.为了避免求解rUB方程,20世纪90年代,Freeman等人系统地提出了逆最优控制问题[5-7J,它不是使在最优控制设计之前所提出的目标泛函取得极小值,相反,而是使一推得的目标泛函取极小值,这个推得的目标泛函与最优控制策略有关.这样,寻求最优控制策略和Lyapunov函数结合在一起,就形成了所谓控制Lyapunov函数(以下简称CLF)的概念.逆最优控制的基本思想是:对于非线性控制系统,HJB方程稳定的状态解是一个CLF.这样,求解HJB方程就转变为寻求闭环系统的CLF.1963年,美国气象学家Lorenz在研究大气对流时,提出了着名的Lorenz方程J,揭开了混沌研究的序幕.1999年,陈关荣发现了一个类似但不拓扑等价的混沌吸引子,称为Chen吸引子J.2002 年,吕金虎等人发现在这二个对耦系统之间存在一-…t--‟,N的混沌系统,称为系统【10,hi.最近,文献[12]提出了一种新的四维混沌系统,随着参数的取值不同,可以观察到非常复杂的混沌动力学行为和千奇百怪的混沌分叉现象.本文基于Lyapunov稳定性理论,应用逆最优控制方法为这种四维混沌系统设计了一个线性状态反馈控制器.采用理论证明和数值模拟表明该控制器的有效性.1问题的描述文献[12]提出的四维混沌系统的数学模型为1=口(z2一z1)+/‟2/‟34,]{z6(z?_zz)一?,,}(1)3一一CX31-工1X24‟lX4一d.z-4+X1.;E2X3.J其中,x=(1,2,z3,4)T∈R4是系统的状态变量,a,b,C,d是系统的已知参数.它们必须满足条件:a,b,C,d>0,b一(a+c+d)<0.根据参数取值的不同,系统(1)有65个不稳定的平衡点:So=(0,0,0,0),Sk(z,,,);走=1,...,64;i=1,...,8;J=1, (8)其中,11=±了,3=±,51=±,=±可,收稿日期:2o05—07—07基金项目:国家自然科学基金资助项目(60274017,60325311);高等学校博士学科点专项科研基金资助项目(2o011o45023).作者简介:谢英慧(1972一),女,吉林省吉林市人,东北大学博士研究生,沈阳炮兵学院讲师;张化光(1959一),男,吉林省吉林市人,东北大学教授.博士生导师.第3期谢英慧等:一种四维混沌系统的逆最优控制249:±i,=±吉:,吐:±—,q=~/,P=,/口+6ab+b.在系统(1)中取参数a=30,b:10,C=37,d=10,初值x0=[一10,10,10,20],系统(1)将产生混沌现象,如图1所示.为了使混沌系统能够全局渐近稳定到系统的零平衡点,应用逆最优控制方法为这种四维混沌系统设计了一个线性状态反馈控制器.图1当a=30.b=10.C=37.d=10时.四维混沌系统的X1oX2oX3相轨迹图Fig.111‟eX1一X2~X3Dhasetrajectoryof4-Dchaotic systemwhena=30.b=10-C=37-d=102逆最优控制器的设计定理通过线性状态反馈控制器“=一(6b++1),(2)系统(1)能够被全局渐近稳定到零平衡点.证明设受控的四维混沌系统为l=a(x2一1)+x2x3x4,126(_x2)一XlX3X4+”,}(3)3一一CX3-r1X24‟fX4一dx4+IX2x3?j式中,”为控制器.构造如下的Lyapunov函数:V=12l+3x+;+;).(4)对V求导,得==(厂(x)+g(跏)=LfV+(V)H.(5)其中,X=(l,2,3,4)T,g(x)=(0,3,0,0)T,,(x)=(a(x2一1)+x25c3x4,36(Xl+or2)一3XlX3:r4,一cx3+xix2..r4,一dx4+lX2X3),L,V(LV全豢(LfV:一口(.一)一1旺;一如+(36+2f-Lgv:32.J(6)将式(6)代人式(5)中得=一日(.一凹;一如+(36+);+3z.(7)在式(7)中很容易推得:当L V=0,则L,v<0. 设计如下简单的线性状态反馈控制器:H=一(x)一(V)=一(6++走.).(8)式中,是大于0的常数,R(x):吉(6++k0),k0>0是待求的.将式(8)代人式(7)中得:一口(.一z凹;一如一(3)?从上式中可知:若X≠O,有<0.即控制律(8) 能使受控系统(3)全局渐近稳定.基于逆最优控制的基本思想,同时为了确定走0,下面定义一个目标泛函:(H):{2(x)+I(t(x)+HTR(x)H)dr}.(9其中,z(x)=一2l厂v+R(x)一(LgV)>0. (10)将式(6)代人式(10)中得z(x)=2口(.一)+2c;+2雄一2~(3b+);+卢(6++走.)2.(11)为了使l()>0,取走.=56++1,(12)东北大学(自然科学版)第27卷则式…)为z(x)=2aft(旷22c;+2dt~c+;>0成立.将式(8)代入式(5)中得=LfV一(x)一(LgV).(13)将式(13)两边同乘一2得一21;,=一2flLrV+2R(x)～(L V). (14)将式(10)代入式(14)中得一2=l(X)+R(x)(L V).(15)又由式(8)可知:llTR(x)ll=R(x)一(L V).(16)将式(16)代入式(15)中得Z(X)+llTR(X)ll=一2.(17)将式(17)代入式(9)中得』}1.,(11)=lim{2/W(X(￡))+I(一2)drf= 2flv(x(0)).(18)所以对于最优控制律(8),目标泛函(11)的极小值为mi(11)=2/~(X(O)).将式(12)代入式(8)得最优控制律“:一(6b++1).(19)证毕.3数值仿真为了验证线性状态反馈控制器(2)的控制能力,当系统(1)取参数a=30,b=10,f=37,d=10,初值x0=[一10,10,10,20]时,系统(1)产生混沌现象.此时,控制器U=一1212.图2展示一2O图2当a=30.b=10.C=37.d=10时受控系统(1)在不同初始条件下全局渐近稳定到零平衡点Fig.2111econtrolledchaoticsysternI1)whena=30- b=10.C=37.d=10anditisstabilizedglobally asymptoticallytoreturntozerobalancepoint urlderdifferentinitiaIconditions可以迅速地趋于系统的零平衡点.若系统(1)取参数a=35,b=10,f=1,d=10,初值为x0=[3,3,3,3],系统(1)也产生混沌现象,如图3所示.此时,控制器”=一2.图4展示了在不同的初始条件下,受控系统(1)的混沌轨道同样可以迅速地趋于系统的零平衡点.图3当a=35.b=10.C=1.d=10时四维混沌系统的相轨迹图Fig.3Phasetrajectoryof4-Dchaoticsystemwhena=35.b=10.C=1.d=10lI—302520嚣15105品一2O图4当a=35.b=10.C=1.d=10时受控系统(1)在不同初始条件下全局渐近稳定到零平衡点Fig.4Thecontrolledchaoticsystern(1)whena=35.b=10.C=1.d=10anditisstabilized globallyasymptoticallytoreturntozerobalancepointurlderdifferentinitiaIconditions4结论本文应用逆最优控制方法为四维混沌系统设计了一个线性状态反馈控制器.采用Lyapunov稳定性理论证明所设计的控制器能够使受控系统全局渐近稳定到系统的零平衡点.数值仿真表明,这种逆最优控制方法实用有效,易于实现.在不同的初始条件下,可以迅速将受控四维混沌系统控制到系统的零平衡点.这种方法比其他混沌控制方法简单有效,且容易推广到其他复杂的混沌系统.参考文献:[1]HongYG,QinHS.Adaptivesynchronizationofchaotic systemsviastateoroutputfeedbackcontrol[J].IntJBifurc Chaos,2001,11(4):l149—1158.[2]FematR,JoseAR,GuillermoFA.Adaptivesynchroniza.第3期谢英慧等:一种四维混沌系统的逆最优控制251 tionofhigh—orderchaoticsysterrLs:afeedbackwith1oW—order parameterization[J].PhysicaD,2000,139(3):231—246. LiaoTL.TsaiSH.Adaptivesynchronizationofchaoticsystero~sanditsapplicationtOsecurecommunicationlJJ.Ch口Solitons&Fractals,2000,l1(9):1387—1396.LuJA,Ta0CH,LJH,口.Prameteridentification andtrackingofanunifiedsystem[J].ChinLet,2002,19(5):632.FreemanRA.KokotovicPV.Inverseoptimalityinrobuststabilization[Jj.SIAMJournal01lControlandOptimization,1996,34:1365—1391.KrsticM.LiZH.Inverseoptimaldesignofinput.to-state stabilizingnonlinearoontrollers[J1.1EEETm?/SAutomaticControl,1998,43(3):336—350.SanchezEN,PrezJP,MartinezM,ela1.Chaosstabilization:aninverseoptimalcontrolapproach[J].Latin AmerAppRes:lntJ,2002,32:l11一l14.[8]LorenzEN.Deterministicnon-periodicflows[J].AtomsSci.1963,20:130—141.[9]ChenGR,UetaT.Y etanotherchaoticattractor[J].IntJBifurc口.1999,9:1465—1466.[10]uJH,ChenGR.Anewchaoticattractoreoined[J].1ntJBircChaos.2002,12:659—661.[11]LJH,ChenGR,ZhangSC.DynamicalanaX/EYing-hui,ZHANGHua—g uang(SchoolofInformationScience&Engineering,NortheastemUniversity. Shenyang110004,China.Correspondent:XIEYing-hui,E-mail:***************)Abstract:AlinearstatefeedbackcontrolleriSdesignedforcontrollingafour-di mensionalchaoticsystembytheinverseoptimal controllingapproach.BasedontheLyapunovstabilitytheory,thedesignedcont rollerisprovedenabletogloballystabilize asymptoticallythecontrolledsystemtoretumtoitszerobalancepointandminim izethepropw~COstfunctiona1.Twosetsof datafromnuiTlericalsimulationshowtheeffectiveness,readinessandrobustne ssofthecontrollerThechaotictraiectoryofthecontrolled4一Dsystemcanbecontrolledtoretumtoitszerohalancepointunderdifferentinitial conditions.Keywords:four-dimensionalchaoticsystem;inverseoptimalcontrol;Lyapun ovstabilitytheory;globalasymptoticalstabilization;costfunctional(Rec~ved/y7,2005):待发表文章f一『摘要预报口一种基于动态分级网关代理的移动IP缓存方案薛建生,王光兴研究移动IP下平滑切换的缓存方案.首先提出了一种动态分级的网关代理模型,分析了在这个模型下的缓存过程,研究了缓存区的分配与管理,并进行了仿真测试.理论和仿真分析表明,将缓存分为网关代理和局部代理两级,局部代理动态形成,使缓存任务得以分散.采用的单缓存十字链表的缓存结构,及相应的释放和大小设置策略,有效地解决了移动节点切换丢失数据和TCP性能下降及数据乱序问题.为研究移动IP平滑切换0可题提供了基础.基于SP子空间跟踪的修正的MMSE多用户检测方法汪晋宽,贾利琴,刘志刚,薛桂芹分析比较了多种子空间跟踪算法.复杂度高的特征值分解和奇异值分解不利于工程实现,而低复杂度的PASTd应用于多用户检测导致收敛速度慢并且检测性能差.介绍了sP子空间跟踪算法,利用SP算法跟踪信号子空间求得解调向量,设计了修正的I~‟VISE检测器.与SVDMUD和PASTdMUD两种算法相比,仿真结果显示SPMUD算法收敛速度快,输出信噪比和误码率性能接近SVDMUD算法,并保持了较低的计算复杂度,是一种较好的实现方案.1J1J1J1J1J34567[[[[[。

第一单元1.Condensed matter physics 凝聚态物理2.Atomic, molecular and optical physics 原子、分子、光学物理3.Particle and nuclear physics 粒子与原子核物理4.Astrophysics and physical cosmology 天体物理学和物理宇宙学5.Current research frontiers 当前研究前沿6.natural philosophy 哲学7.natural science 自然科学8.matter 物质9.motion 运动10.space and time 时空11.energy 能量12.force 力13.the universe 宇宙14.academic disciplines 学科15.astronomy 天文学16.chemistry 化学17.mathematics 数学18.biology 生物19.Scientific Revolution 科学革命20.interdisciplinary各学科间的21.biophysics 生物物理22.quantum chemistry 量子化学23.mechanism 机制24.avenues 渠道；大街25.advances 前进26.electromagnetism电磁学27.nuclear physics原子核物理28.domestic appliances家用电器29.nuclear weapons核武器30.thermodynamics热力学31.industrialization工业化32.mechanics力学33.calculus微积分34.the theory of classical mechanics经典力学35.the speed of light 光速36.remarkable卓越的37.chaos混沌38.quantum mechanics量子力学39.statistical mechanics 统计力学40.special relativity狭义相对论41.acoustics声学42.statics静力学43.at rest静止44.kinematics运动学45.causes原因46.dynamics动力学47.solid mechanics 固体力学48.fluid mechanics 流体力学49.continuum mechanics 连续介质力学50.hydrostatics流体静力学51.hydrodynamics流体动力学52.aerodynamics气体动力学53.pneumatics气体力学54.sound 声音55.ultrasonics超声学56.sound waves 声波57.frequency 频率58.bioacoustics生物声学59.electroacoustics电声学60.manipulation操作61.audible听得见的62.electronics电子63.visible light 可见光64.infrared红外线65.ultraviolet radiation 紫外线辐射66.reflection 反射67.refraction折射68.interference干涉69.diffraction衍射70.dispersion色散71.polarization偏振72.Heat 热度73.the internal energy内能74.Electricity 电力75.magnetism磁学76.electric current电流77.magnetic field磁场78.Electrostatics静电学79.electric charges电荷80.electrodynamics电动力学81.magnetostatics静磁学82.poles磁极83.matter and energy 物质和能量84.on the very large or very small scale 非常大或非常小的规模85.atomic and nuclear physics 原子与核物理学86.chemical elements化学元素87.The physics of elementary particles基本粒子88.high-energy physics 高能物理学89.particle accelerators 粒子加速器90.Quantum theory 量子论91.discrete离散92.subatomic原子内plementary互补94.The theory of relativity 相对论95.a frame of reference参考系96.the special theory of relativity 狭义相对论97.general theory of relativity 广义相对论98.gravitation万有引力99.universal law 普遍规律100.absolute time and space 绝对的时间和空间101.space-time 时空ponents组成103.Max Planck 普朗克104.quantum mechanics 量子力学105.probabilistic概率性106.quantum field theory量子场107.dynamical动态的108.curved弯曲的109.massive巨大的110.candidate候选111.quantum gravity 量子重力112.macroscopic宏观113.properties属性114.solids 固体115.liquids 液体116.electromagnetic force电磁力117.atom 原子118.superconducting超导119.conduction electrons 传导电子120.ferromagnetic 铁磁体121.the ferromagnetic and antiferromagnetic phases of spins铁磁和反铁磁的阶段的旋转122.atomic lattices原子晶格123.solid-state physics 固体物理124.subfields分区；子域125.nanotechnology纳米技术126.engineering工程学127.quantum treatments 量子治疗128.Atomic physics 原子物理129.electron shells电子壳层130.trap捕获131.ions离子132.collision碰撞133.nucleus原子核134.hyperfine splitting超精细分裂135.fission and fusion 分裂与融合136.Molecular physics 分子物理137.optical fields 光场138.realm范围139.properties属性140.distinct区别141.Particle physics 粒子物理142.elementary constituents基本成分143.interactions 相互作用144.detectors探测器puter programs程序146.Standard Model 标准模型147.quarks and leptons轻子-夸克148.gauge bosons规范波色子149.gluons胶子150.photons光子151.nuclear power generation核发电152.nuclear weaponsh核武器153.nuclear medicine 核医学154.magnetic resonance imaging磁共振成像155.ion implantation离子注入156.materials engineering 材料工程157.radiocarbon dating放射性碳测定年代158.geology 地质学159.archaeology考古学.160.Astrophysics天体物理学161.astronomy天文学162.stellar structure恒星结构163.stellar evolution恒星演化164.solar system太阳系165.cosmology宇宙学166.disciplines学科167.emitted射出168.celestial bodies天体169.Perturbations扰动170.interference干扰171.Physical cosmology 宇宙物理学172.Hubble diagram哈勃图173.steady state 定态，稳恒态174.Big Bang nucleo-synthesis核合成175.cosmic microwave background宇宙微波背景176.cosmological principle 宇宙论原理；宇宙论原则177.cosmic inflation宇宙膨胀178.dark energy 暗能量179.dark matter暗物质of high-temperature superconductivity 高温超导180.spintronics自旋电子学181.quantum computers 量子电脑182.the Standard Model 标准模型183.neutrinos中微子184.solar太阳185.the TeV万亿电子伏186.the super-symmetric particles 超对称粒子187.quantum gravity 量子重力188.superstring超弦189.theory and loop圈190.ultra-high energy cosmic rays高能宇宙射线,191.the baryon asymmetry重子不对称,192.the acceleration of the universe and the anomalous宇宙的加速和异常193.rotation旋转194.galaxies星系.195.turbulence动荡196.water droplets 水滴197.mechanisms of surface tension catastrophes表面紧张灾难198.heterogeneous多相的199.aerodynamics 气体力学第二单元所有的红色单词，重要的我标有星号1.classical mechanics 经典力学*2.physical laws 物理定律3.forces 力4.macroscopic 宏观的5.Projectiles 抛射体6.Spacecraft 太空飞船7.Planets 行星8.Stars 恒星9.Galaxies 星系,银河系10.gases, liquids, solids 气体,液体固体11.the speed of light 光速12.quantum mechanics 量子力学*13.the atomic nature of matter 物质的原子性质14.wave–particle duality 波粒二象性*15.special relativity 狭义相对论*16.General relativity 广义相对论*17.Newton's law of universal gravitation 牛顿万有引力*18.Newtonian mechanics 牛顿力学*grangian mechanics 拉格朗日力学*20.Hamiltonian mechanics 哈密顿力学*21.analytical mechanics 分析力学*22.as point particles 质点*23.Negligible 微不足道的可忽略的24.position, mass 位置,质量25.Forces 力26.non-zero size 不计形状27.the electron 电子*28.quantum mechanics 量子力学*29.degrees of freedom 自由度*30.Spin 旋转posite 组合的32.center of mass 质心33.the principle of locality 局部性原理34.Position 位置35.reference point 参照点(参照物)*36.in space 在空间37.Origin 原点*38.the vector 矢量39.Particle 质点*40.Function 函数41.Galilean relativity 伽利略相对性原理*42.Absolute 绝对43.time interval 时间间隔44.Euclidean geometry 欧几里得几何学45.Velocity 速度46.rate of change 变化率47.Derivative 倒数*48.Vector 矢量49.Speed 速度50.Acceleration 加速度*51.second derivative 二阶导*52.Magnitude 大小(量级)53.the direction 方向54.or both55.Deceleration 加速度56.Observer 观察者57.reference frames 参考系*58.inertial frames 惯性系*59.at rest60.in a state of uniform motion 运动状态一致61.Straight 直的62.physical laws 物理学定理63.non-inertial 非惯性系64.accelerating 加速65.fictitious forces 虚拟力(达朗贝尔力)*66.equations of motion 运动学方程*67.the distant stars 遥远的恒星68.Newton 牛顿69.force and momentum 力和动量70.Newton's second law of motion 牛顿第二定律*71.(canonical) momentum 动量* force 净力73.ordinary differential equation 常微分方程*74.the equation of motion 运动学方程*75.gravitational force 重力*76.Lorentz force 洛伦兹力*77.Electromagnetism 电磁学*78.Newton's third law 牛顿第三定律*79.opposite reaction force 反作用力80.along the line 沿直线81.displacement 位移*82.work done 做功83.scalar product 标极*84.the line integral 线积分*85.path 路径86.conservative. 守恒*87.Gravity 重力88.Hooke's law 胡克定律*89.Friction 摩擦力*90.kinetic energy 动能*91.work–energy theorem 功能关系(动能定理)*92.the change in kinetic energy 动能改变量93.gradient 梯度*94.potential energy 势能*95.Conservative 保守的,守恒的96.potential energy 势能97.total energy 总能量(机械能)*98.conservation of energy 能量守恒**99.linear momentum 线动量100.translational momentum 平移动量101.closed system 封闭系统*102.external forces 外力*103.total linear momentum 总(线)动量线动量就是动量区别于角动量104.center of mass 质心*105.Euler's first law 欧拉第一定律106.elastic collision 弹性碰撞*107.inelastic collision 非弹性碰撞*108.slingshot maneuver 弹弓机动109.Rigidity 硬度(刚性)*110.Dissipation 损耗**111.inelastic collision 非弹性碰撞112.heat or sound 热或声113.new particles 新粒子114.angular momentum 角动量*115.moment of momentum 瞬时动量*116.rotational inertia 转动惯量*117.rotational velocity 转速*118.rigid body 刚体**119.moment of inertia 惯性力矩*120.angular velocity 角速度*121.linear momentum 线动量122.Crossed 叉乘*123.Position 位置124.angular momentum 角动量125.pseudo-vector 赝矢量*126.right-hand rule 右手规则 external torque 净外力转矩128.neutron stars 中子星129.angular momentum 角动量*130.Conservation 守恒131.Gyrocompass 陀螺罗盘132.no external torque 无外力炬133.Isotropy 各向同性*134.Torque 转矩135.central force motion 中心力移动136.white dwarfs, neutron stars and black holes 白矮星,中子星,黑洞第三单元ThermodynamicsThermodynamics: 热力学；热力的Heat ：热；热力；热度Work：功macroscopic variables：肉眼可见的；宏观的，粗观的，粗显的。

More informationNONLINEAR TIME SERIES ANALYSISThis book represents a modern approach to time series analysis which is based onthe theory of dynamical systems.It starts from a sound outline of the underlyingtheory to arrive at very practical issues,which are illustrated using a large number ofempirical data sets taken from variousfields.This book will hence be highly usefulfor scientists and engineers from all disciplines who study time variable signals,including the earth,life and social sciences.The paradigm of deterministic chaos has influenced thinking in manyfields ofscience.Chaotic systems show rich and surprising mathematical structures.In theapplied sciences,deterministic chaos provides a striking explanation for irregulartemporal behaviour and anomalies in systems which do not seem to be inherentlystochastic.The most direct link between chaos theory and the real world is the anal-ysis of time series from real systems in terms of nonlinear dynamics.Experimentaltechnique and data analysis have seen such dramatic progress that,by now,mostfundamental properties of nonlinear dynamical systems have been observed in thelaboratory.Great efforts are being made to exploit ideas from chaos theory where-ver the data display more structure than can be captured by traditional methods.Problems of this kind are typical in biology and physiology but also in geophysics,economics and many other sciences.This revised edition has been significantly rewritten an expanded,includingseveral new chapters.In view of applications,the most relevant novelties will be thetreatment of non-stationary data sets and of nonlinear stochastic processes insidethe framework of a state space reconstruction by the method of delays.Hence,non-linear time series analysis has left the rather narrow niche of strictly deterministicsystems.Moreover,the analysis of multivariate data sets has gained more atten-tion.For a direct application of the methods of this book to the reader’s own datasets,this book closely refers to the publicly available software package TISEAN.The availability of this software will facilitate the solution of the exercises,so thatreaders now can easily gain their own experience with the analysis of data sets.Holger Kantz,born in November1960,received his diploma in physics fromthe University of Wuppertal in January1986with a thesis on transient chaos.InJanuary1989he obtained his Ph.D.in theoretical physics from the same place,having worked under the supervision of Peter Grassberger on Hamiltonian many-particle dynamics.During his postdoctoral time,he spent one year on a Marie Curiefellowship of the European Union at the physics department of the University ofMore informationFlorence in Italy.In January1995he took up an appointment at the newly foundedMax Planck Institute for the Physics of Complex Systems in Dresden,where heestablished the research group‘Nonlinear Dynamics and Time Series Analysis’.In1996he received his venia legendi and in2002he became adjunct professorin theoretical physics at Wuppertal University.In addition to time series analysis,he works on low-and high-dimensional nonlinear dynamics and its applications.More recently,he has been trying to bridge the gap between dynamics and statis-tical physics.He has(co-)authored more than75peer-reviewed articles in scien-tific journals and holds two international patents.For up-to-date information seehttp://www.mpipks-dresden.mpg.de/mpi-doc/kantzgruppe.html.Thomas Schreiber,born1963,did his diploma work with Peter Grassberger atWuppertal University on phase transitions and information transport in spatio-temporal chaos.He joined the chaos group of Predrag Cvitanovi´c at the Niels BohrInstitute in Copenhagen to study periodic orbit theory of diffusion and anomaloustransport.There he also developed a strong interest in real-world applications ofchaos theory,leading to his Ph.D.thesis on nonlinear time series analysis(Univer-sity of Wuppertal,1994).As a research assistant at Wuppertal University and duringseveral extended appointments at the Max Planck Institute for the Physics of Com-plex Systems in Dresden he published numerous research articles on time seriesmethods and applications ranging from physiology to the stock market.His habil-itation thesis(University of Wuppertal)appeared as a review in Physics Reportsin1999.Thomas Schreiber has extensive experience teaching nonlinear dynamicsto students and experts from variousfields and at all levels.Recently,he has leftacademia to undertake industrial research.NONLINEAR TIME SERIES ANALYSIS HOLGER KANTZ AND THOMAS SCHREIBERMax Planck Institute for the Physics of Complex Systems,DresdenMore informationMore informationpublished by the press syndicate of the university of cambridgeThe Pitt Building,Trumpington Street,Cambridge,United Kingdomcambridge university pressThe Edinburgh Building,Cambridge CB22RU,UK40West20th Street,New York,NY10011–4211,USA477Williamstown Road,Port Melbourne,VIC3207,AustraliaRuiz de Alarc´o n13,28014Madrid,SpainDock House,The Waterfront,Cape Town8001,South AfricaC Holger Kantz and Thomas Schreiber,2000,2003This book is in copyright.Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,no reproduction of any part may take place withoutthe written permission of Cambridge University Press.First published2000Second edition published2003Printed in the United Kingdom at the University Press,CambridgeTypeface Times11/14pt.System L A T E X2ε[tb]A catalogue record for this book is available from the British LibraryLibrary of Congress Cataloguing in Publication dataKantz,Holger,1960–Nonlinear time series analysis/Holger Kantz and Thomas Schreiber.–[2nd ed.].p.cm.Includes bibliographical references and index.ISBN0521821509–ISBN0521529026(paperback)1.Time-series analysis.2.Nonlinear theories.I.Schreiber,Thomas,1963–II.TitleQA280.K3552003519.5 5–dc212003044031ISBN0521821509hardbackISBN0521529026paperbackThe publisher has used its best endeavours to ensure that the URLs for external websites referred to in this bookare correct and active at the time of going to press.However,the publisher has no responsibility for the websites and can make no guarantee that a site will remain live or that the content is or will remain appropriate.More informationContentsPreface to thefirst edition page xiPreface to the second edition xiiiAcknowledgements xvI Basic topics11Introduction:why nonlinear methods?32Linear tools and general considerations132.1Stationarity and sampling132.2Testing for stationarity152.3Linear correlations and the power spectrum182.3.1Stationarity and the low-frequency component in thepower spectrum232.4Linearfilters242.5Linear predictions273Phase space methods303.1Determinism:uniqueness in phase space303.2Delay reconstruction353.3Finding a good embedding363.3.1False neighbours373.3.2The time lag393.4Visual inspection of data393.5Poincar´e surface of section413.6Recurrence plots434Determinism and predictability484.1Sources of predictability484.2Simple nonlinear prediction algorithm504.3Verification of successful prediction534.4Cross-prediction errors:probing stationarity564.5Simple nonlinear noise reduction58vMore informationvi Contents5Instability:Lyapunov exponents655.1Sensitive dependence on initial conditions655.2Exponential divergence665.3Measuring the maximal exponent from data696Self-similarity:dimensions756.1Attractor geometry and fractals756.2Correlation dimension776.3Correlation sum from a time series786.4Interpretation and pitfalls826.5Temporal correlations,non-stationarity,and space timeseparation plots876.6Practical considerations916.7A useful application:determination of the noise level using thecorrelation integral926.8Multi-scale or self-similar signals956.8.1Scaling laws966.8.2Detrendedfluctuation analysis1007Using nonlinear methods when determinism is weak1057.1Testing for nonlinearity with surrogate data1077.1.1The null hypothesis1097.1.2How to make surrogate data sets1107.1.3Which statistics to use1137.1.4What can go wrong1157.1.5What we have learned1177.2Nonlinear statistics for system discrimination1187.3Extracting qualitative information from a time series1218Selected nonlinear phenomena1268.1Robustness and limit cycles1268.2Coexistence of attractors1288.3Transients1288.4Intermittency1298.5Structural stability1338.6Bifurcations1358.7Quasi-periodicity139II Advanced topics1419Advanced embedding methods1439.1Embedding theorems1439.1.1Whitney’s embedding theorem1449.1.2Takens’s delay embedding theorem1469.2The time lag148More informationContents vii9.3Filtered delay embeddings1529.3.1Derivative coordinates1529.3.2Principal component analysis1549.4Fluctuating time intervals1589.5Multichannel measurements1599.5.1Equivalent variables at different positions1609.5.2Variables with different physical meanings1619.5.3Distributed systems1619.6Embedding of interspike intervals1629.7High dimensional chaos and the limitations of the time delayembedding1659.8Embedding for systems with time delayed feedback17110Chaotic data and noise17410.1Measurement noise and dynamical noise17410.2Effects of noise17510.3Nonlinear noise reduction17810.3.1Noise reduction by gradient descent17910.3.2Local projective noise reduction18010.3.3Implementation of locally projective noise reduction18310.3.4How much noise is taken out?18610.3.5Consistency tests19110.4An application:foetal ECG extraction19311More about invariant quantities19711.1Ergodicity and strange attractors19711.2Lyapunov exponents II19911.2.1The spectrum of Lyapunov exponents and invariantmanifolds20011.2.2Flows versus maps20211.2.3Tangent space method20311.2.4Spurious exponents20511.2.5Almost two dimensionalflows21111.3Dimensions II21211.3.1Generalised dimensions,multi-fractals21311.3.2Information dimension from a time series21511.4Entropies21711.4.1Chaos and theflow of information21711.4.2Entropies of a static distribution21811.4.3The Kolmogorov–Sinai entropy22011.4.4The -entropy per unit time22211.4.5Entropies from time series data226More informationviii Contents11.5How things are related22911.5.1Pesin’s identity22911.5.2Kaplan–Yorke conjecture23112Modelling and forecasting23412.1Linear stochastic models andfilters23612.1.1Linearfilters23712.1.2Nonlinearfilters23912.2Deterministic dynamics24012.3Local methods in phase space24112.3.1Almost model free methods24112.3.2Local linearfits24212.4Global nonlinear models24412.4.1Polynomials24412.4.2Radial basis functions24512.4.3Neural networks24612.4.4What to do in practice24812.5Improved cost functions24912.5.1Overfitting and model costs24912.5.2The errors-in-variables problem25112.5.3Modelling versus prediction25312.6Model verification25312.7Nonlinear stochastic processes from data25612.7.1Fokker–Planck equations from data25712.7.2Markov chains in embedding space25912.7.3No embedding theorem for Markov chains26012.7.4Predictions for Markov chain data26112.7.5Modelling Markov chain data26212.7.6Choosing embedding parameters for Markov chains26312.7.7Application:prediction of surface wind velocities26412.8Predicting prediction errors26712.8.1Predictability map26712.8.2Individual error prediction26812.9Multi-step predictions versus iterated one-step predictions27113Non-stationary signals27513.1Detecting non-stationarity27613.1.1Making non-stationary data stationary27913.2Over-embedding28013.2.1Deterministic systems with parameter drift28013.2.2Markov chain with parameter drift28113.2.3Data analysis in over-embedding spaces283More informationContents ix13.2.4Application:noise reduction for human voice28613.3Parameter spaces from data28814Coupling and synchronisation of nonlinear systems29214.1Measures for interdependence29214.2Transfer entropy29714.3Synchronisation29915Chaos control30415.1Unstable periodic orbits and their invariant manifolds30615.1.1Locating periodic orbits30615.1.2Stable/unstable manifolds from data31215.2OGY-control and derivates31315.3Variants of OGY-control31615.4Delayed feedback31715.5Tracking31815.6Related aspects319A Using the TISEAN programs321A.1Information relevant to most of the routines322A.1.1Efficient neighbour searching322A.1.2Re-occurring command options325A.2Second-order statistics and linear models326A.3Phase space tools327A.4Prediction and modelling329A.4.1Locally constant predictor329A.4.2Locally linear prediction329A.4.3Global nonlinear models330A.5Lyapunov exponents331A.6Dimensions and entropies331A.6.1The correlation sum331A.6.2Information dimension,fixed mass algorithm332A.6.3Entropies333A.7Surrogate data and test statistics334A.8Noise reduction335A.9Finding unstable periodic orbits336A.10Multivariate data336B Description of the experimental data sets338B.1Lorenz-like chaos in an NH3laser338B.2Chaos in a periodically modulated NMR laser340B.3Vibrating string342B.4Taylor–Couetteflow342B.5Multichannel physiological data343More informationx ContentsB.6Heart rate during atrialfibrillation343B.7Human electrocardiogram(ECG)344B.8Phonation data345B.9Postural control data345B.10Autonomous CO2laser with feedback345B.11Nonlinear electric resonance circuit346B.12Frequency doubling solid state laser348B.13Surface wind velocities349References350Index365More informationPreface to thefirst editionThe paradigm of deterministic chaos has influenced thinking in manyfields of sci-ence.As mathematical objects,chaotic systems show rich and surprising structures.Most appealing for researchers in the applied sciences is the fact that determinis-tic chaos provides a striking explanation for irregular behaviour and anomalies insystems which do not seem to be inherently stochastic.The most direct link between chaos theory and the real world is the analysis oftime series from real systems in terms of nonlinear dynamics.On the one hand,experimental technique and data analysis have seen such dramatic progress that,by now,most fundamental properties of nonlinear dynamical systems have beenobserved in the laboratory.On the other hand,great efforts are being made to exploitideas from chaos theory in cases where the system is not necessarily deterministicbut the data displays more structure than can be captured by traditional methods.Problems of this kind are typical in biology and physiology but also in geophysics,economics,and many other sciences.In all thesefields,even simple models,be they microscopic or phenomenological,can create extremely complicated dynamics.How can one verify that one’s model isa good counterpart to the equally complicated signal that one receives from nature?Very often,good models are lacking and one has to study the system just from theobservations made in a single time series,which is the case for most non-laboratorysystems in particular.The theory of nonlinear dynamical systems provides new toolsand quantities for the characterisation of irregular time series data.The scope ofthese methods ranges from invariants such as Lyapunov exponents and dimensionswhich yield an accurate description of the structure of a system(provided thedata are of high quality)to statistical techniques which allow for classification anddiagnosis even in situations where determinism is almost lacking.This book provides the experimental researcher in nonlinear dynamics with meth-ods for processing,enhancing,and analysing the measured signals.The theorist willbe offered discussions about the practical applicability of mathematical results.ThexiMore informationxii Preface to thefirst editiontime series analyst in economics,meteorology,and otherfields willfind inspira-tion for the development of new prediction algorithms.Some of the techniquespresented here have also been considered as possible diagnostic tools in clinical re-search.We will adopt a critical but constructive point of view,pointing out ways ofobtaining more meaningful results with limited data.We hope that everybody whohas a time series problem which cannot be solved by traditional,linear methodswillfind inspiring material in this book.Dresden and WuppertalNovember1996More informationPreface to the second editionIn afield as dynamic as nonlinear science,new ideas,methods and experimentsemerge constantly and the focus of interest shifts accordingly.There is a continuousstream of new results,and existing knowledge is seen from a different angle aftervery few years.Five years after thefirst edition of“Nonlinear Time Series Analysis”we feel that thefield has matured in a way that deserves being reflected in a secondedition.The modification that is most immediately visible is that the program listingshave been be replaced by a thorough discussion of the publicly available softwareTISEAN.Already a few months after thefirst edition appeared,it became clearthat most users would need something more convenient to use than the bare libraryroutines printed in the book.Thus,together with Rainer Hegger we prepared stand-alone routines based on the book but with input/output functionality and advancedfeatures.Thefirst public release was made available in1998and subsequent releasesare in widespread use now.Today,TISEAN is a mature piece of software thatcovers much more than the programs we gave in thefirst edition.Now,readerscan immediately apply most methods studied in the book on their own data usingTISEAN programs.By replacing the somewhat terse program listings by minuteinstructions of the proper use of the TISEAN routines,the link between book andsoftware is strengthened,supposedly to the benefit of the readers and users.Hencewe recommend a download and installation of the package,such that the exercisescan be readily done by help of these ready-to-use routines.The current edition has be extended in view of enlarging the class of data sets to betreated.The core idea of phase space reconstruction was inspired by the analysis ofdeterministic chaotic data.In contrast to many expectations,purely deterministicand low-dimensional data are rare,and most data fromfield measurements areevidently of different nature.Hence,it was an effort of our scientific work over thepast years,and it was a guiding concept for the revision of this book,to explore thepossibilities to treat other than purely deterministic data sets.xiiiMore informationxiv Preface to the second editionThere is a whole new chapter on non-stationary time series.While detectingnon-stationarity is still briefly discussed early on in the book,methods to deal withmanifestly non-stationary sequences are described in some detail in the secondpart.As an illustration,a data source of lasting interest,human speech,is used.Also,a new chapter deals with concepts of synchrony between systems,linear andnonlinear correlations,information transfer,and phase synchronisation.Recent attempts on modelling nonlinear stochastic processes are discussed inChapter12.The theoretical framework forfitting Fokker–Planck equations to datawill be reviewed and evaluated.While Chapter9presents some progress that hasbeen made in modelling input–output systems with stochastic but observed inputand on the embedding of time delayed feedback systems,the chapter on mod-elling considers a data driven phase space approach towards Markov chains.Windspeed measurements are used as data which are best considered to be of nonlinearstochastic nature despite the fact that a physically adequate mathematical model isthe deterministic Navier–Stokes equation.In the chapter on invariant quantities,new material on entropy has been included,mainly on the -and continuous entropies.Estimation problems for stochastic ver-sus deterministic data and data with multiple length and time scales are discussed.Since more and more experiments now yield good multivariate data,alternativesto time delay embedding using multiple probe measurements are considered at var-ious places in the text.This new development is also reflected in the functionalityof the TISEAN programs.A new multivariate data set from a nonlinear semicon-ductor electronic circuit is introduced and used in several places.In particular,adifferential equation has been successfully established for this system by analysingthe data set.Among other smaller rearrangements,the material from the former chapter“Other selected topics”,has been relocated to places in the text where a connectioncan be made more naturally.High dimensional and spatio-temporal data is now dis-cussed in the context of embedding.We discuss multi-scale and self-similar signalsnow in a more appropriate way right after fractal sets,and include recent techniquesto analyse power law correlations,for example detrendedfluctuation analysis.Of course,many new publications have appeared since1997which are potentiallyrelevant to the scope of this book.At least two new monographs are concerned withthe same topic and a number of review articles.The bibliography has been updatedbut remains a selection not unaffected by personal preferences.We hope that the extended book will prove its usefulness in many applicationsof the methods and further stimulate thefield of time series analysis.DresdenDecember2002More informationAcknowledgementsIf there is any feature of this book that we are proud of,it is the fact that almost allthe methods are illustrated with real,experimental data.However,this is anythingbut our own achievement–we exploited other people’s work.Thus we are deeplyindebted to the experimental groups who supplied data sets and granted permissionto use them in this book.The production of every one of these data sets requiredskills,experience,and equipment that we ourselves do not have,not forgetting thehours and hours of work spent in the laboratory.We appreciate the generosity ofthe following experimental groups:NMR laser.Our contact persons at the Institute for Physics at Z¨u rich University were Leci Flepp and Joe Simonet;the head of the experimental group is E.Brun.(See AppendixB.2.)Vibrating string.Data were provided by Tim Molteno and Nick Tufillaro,Otago University, Dunedin,New Zealand.(See Appendix B.3.)Taylor–Couetteflow.The experiment was carried out at the Institute for Applied Physics at Kiel University by Thorsten Buzug and Gerd Pfister.(See Appendix B.4.) Atrialfibrillation.This data set is taken from the MIT-BIH Arrhythmia Database,collected by G.B.Moody and R.Mark at Beth Israel Hospital in Boston.(See Appendix B.6.) Human ECG.The ECG recordings we used were taken by Petr Saparin at Saratov State University.(See Appendix B.7.)Foetal ECG.We used noninvasively recorded(human)foetal ECGs taken by John F.Hofmeister as the Department of Obstetrics and Gynecology,University of Colorado,Denver CO.(See Appendix B.7.)Phonation data.This data set was made available by Hanspeter Herzel at the Technical University in Berlin.(See Appendix B.8.)Human posture data.The time series was provided by Steven Boker and Bennett Bertenthal at the Department of Psychology,University of Virginia,Charlottesville V A.(SeeAppendix B.9.)xvMore informationxvi AcknowledgementsAutonomous CO2laser with feedback.The data were taken by Riccardo Meucci and Marco Ciofini at the INO in Firenze,Italy.(See Appendix B.10.)Nonlinear electric resonance circuit.The experiment was designed and operated by M.Diestelhorst at the University of Halle,Germany.(See Appendix B.11.)Nd:YAG laser.The data we use were recorded in the University of Oldenburg,where we wish to thank Achim Kittel,Falk Lange,Tobias Letz,and J¨u rgen Parisi.(See AppendixB.12.)We used the following data sets published for the Santa Fe Institute Time SeriesContest,which was organised by Neil Gershenfeld and Andreas Weigend in1991:NH3laser.We used data set A and its continuation,which was published after the contest was closed.The data was supplied by U.H¨u bner,N.B.Abraham,and C.O.Weiss.(SeeAppendix B.1.)Human breath rate.The data we used is part of data set B of the contest.It was submitted by Ari Goldberger and coworkers.(See Appendix B.5.)During the composition of the text we asked various people to read all or part of themanuscript.The responses ranged from general encouragement to detailed technicalcomments.In particular we thank Peter Grassberger,James Theiler,Daniel Kaplan,Ulrich Parlitz,and Martin Wiesenfeld for their helpful remarks.Members of ourresearch groups who either contributed by joint work to our experience and knowl-edge or who volunteered to check the correctness of the text are Rainer Hegger,Andreas Schmitz,Marcus Richter,Mario Ragwitz,Frank Schm¨u ser,RathinaswamyBhavanan Govindan,and Sharon Sessions.We have also considerably profited fromcomments and remarks of the readers of thefirst edition of the book.Their effortin writing to us is gratefully appreciated.Last but not least we acknowledge the encouragement and support by SimonCapelin from Cambridge University Press and the excellent help in questions ofstyle and English grammar by Sheila Shepherd.。

Stability and Control:Theory,Methods and ApplicationsVolume 22 Dynamical Systems and ControlE DITED BYFirdaus E. UdwadiaUniversity of Southern CaliforniaUSAH. I. WeberPontifical Catholic University of Rio de JaneiroBrazilGeorge LeitmannUniversity of California, BerkeleyUSACHAPMAN & HALL/CRCA CRC Press CompanyBoca Raton London New Y ork Washington, D.C.ContentsList of contributorsPrefacePart IA geometric approach to the mechanics of densely folded mediaLuiz BevilacquaOn a general principle of mechanics and its application to general non-ideal nonholonomic constraintsFirdaus E.UdwadiaMathematical analysis of vibrations of nonhomogeneousfilament with one end loadMarianna A.ShubovExpanded point mapping analysis of periodic systemsHenryk Flashner and Michael GolatA preliminary analysis of the phase portrait’s structure ofa nonlinear pendulum-mechanical system using the perturbedHamiltonian formulationD´e bora Belato,Hans Ingo Weber and Jos´e Manoel BalthazarA review of rigid-body collision models in the planeEdson Cataldo and Rubens SampaioPart IIOptimal round-trip Earth–Mars trajectories for roboticflight and mannedflightA.Miele,T.Wang and S.MancusoAircraft take-offin windshear:a viability approachN.Seube,R.Moitie and G.LeitmannStability of torsional and vertical motion of suspension bridges subject to stochastic wind forcesN.U.AhmedCopyright © 2004 CRC Press, LLCTime delayed control of structural systemsFirdaus E.Udwadia,Hubertus F.von Bremen,Ravi Kumarand Mohamed HosseiniRobust real-and discrete-time control of a steer-by-wire system in cars Eduard ReithmeierOptimal placement of piezoelectric sensor/actuators for smart structures vibration controlVicente Lopes,Jr.,Valder Steffen,Jr.and Daniel J.InmanA review of new vibration issues due to non-ideal energy sourcesJ.M.Balthazar,R.M.L.R.F Brasil,H.I.Weber,A.Fenili,D.Belato,J.L.P.Felix and F.J.GarzelliIdentification offlexural stiffness parameters of beamsJos´e Jo˜a o de Esp´ındola and Jo˜a o Morais da Silva Neto Active noise control caused by airflow through a rectangular duct Seyyed Said Dana,Naor Moraes Melo and Simplicio Arnaudda SilvaDynamical features of an autonomous two-bodyfloating system Helio Mitio Morishita and Jess´e Rebello de Souza Junior Dynamics and control of aflexible rotating arm throughthe movement of a sliding massAgenor de Toledo Fleury and Frederico Ricardo Ferreirade OliveiraMeasuring chaos in gravitational wavesHumberto Piccoli and Fernando KokubunPart IIIEstimation of the attractor for an uncertain epidemic modelE.Cr¨u ck,N.Seube and G.LeitmannLiar paradox viewed by the fuzzy logic theoryYe-Hwa ChenPareto-improving cheating in an economic policy gameChristophe Deissenberg and Francisco Alvarez Gonzalez Dynamic investment behavior taking into account ageing ofthe capital goodsGustav Feichtinger,Richard F.Hartl,Peter Kortand Vladimir VeliovA mathematical approach towards the issue of synchronizationin neocortical neural networksR.Stoop and D.BlankOptimal control of human posture using algorithms based on consistent approximations theoryLuciano Luporini Menegaldo,Agenor de Toledo Fleuryand Hans Ingo WeberCopyright © 2004 CRC Press, LLCContributorsN.U.Ahmed,School of Information Technology and Engineering,Department of Mathematics,University of Ottawa,Ottawa,OntarioJos´e Manoel Balthazar,Instituto de Geociˆe ncias e Ciˆe ncias Exatas–UNESP–Rio Claro,Caixa Postal178,CEP13500-230,Rio Claro,SP,BrasilD´e bora Belato,DPM–Faculdade de Engenharia Mecˆa nica–UNICAMP,Caixa Postal6122,CEP13083-970,Campinas,SP,BrasilLuiz Bevilacqua,Laborat´o rio Nacional de Computa¸c˜a o Cient´ıfica–LNCC,Av.Get´u lio Vargas333,Rio de Janeiro,RJ25651-070,BrasilD.Blank,Institut f¨u r Neuroinformatik,ETHZ/UNIZH,Winterthurerstraße190,CH-8057Z¨u richR.M.L.R.F.Brasil,Dept.of Structural and Foundations Engineering,Polytech-nic School,University of S˜a o Paulo,P.O.Box61548,05424-930,SP,BrazilEdson Cataldo,Universidade Federal Fluminense(UFF),Departamento de Mate-m´a tica Aplicada,PGMEC-Programa de P´o s-Gradua¸c˜a o em Engenharia Mecˆa nica, Rua M´a rio Santos Braga,S/No-24020,Centro,Niter´o i,RJ,BrasilYe-Hwa Chen,The George W.WoodruffSchool of Mechanical Engineering,Geor-gia Institute of Technology,Atlanta,Georgia30332,USAE.Cr¨u ck,Laboratoire de Recherches Balistiques et A´e rodynamiques,BP914,27207Vernon Cedex,FranceSeyyed Said Dana,Graduate Studies in Mechanical Engineering,Mechanical Engineering Department,Federal University of Paraiba,Campus I,58059-900Joao Pessoa,Paraiba,BrazilChristophe Deissenberg,CEFI,UMR CNRS6126,Universit´e de la M´e diterran´e e (Aix-Marseille II),Chˆa teau La Farge,Route des Milles,13290Les Milles,France Jos´e Jo˜a o de Esp´ındola,Department of Mechanical Engineering,Federal Uni-versity of Santa Catarina,BrazilGustav Feichtinger,Institute for Econometrics,OR and Systems Theory,Uni-versity of Technology,Argentinierstrasse8,A-1040Vienna,AustriaJ.L.P.Felix,School of Mechanical Engineering,UNICAMP,P.O.Box6122,13800-970,Campinas,SP,BrazilA.Fenili,School of Mechanical Engineering,UNICAMP,P.O.Box6122,13800-970,Campinas,SP,BrazilCopyright © 2004 CRC Press, LLCHenryk Flashner,Department of Aerospace and Mechanical Engineering,Uni-versity of Southern California,Los Angeles,CA90089-1453Agenor de Toledo Fleury,Control Systems Group/Mechanical&Electrical En-gineering Division,IPT/S˜a o Paulo State Institute for Technological Research,P.O.Box0141,01064-970,S˜a o Paulo,SP,BrazilF.J.Garzelli,Dept.of Structural and Foundations Engineering,PolytechnicSchool,University of S˜a o Paulo,P.O.Box61548,05424-930,SP,BrazilMichael Golat,Department of Aerospace and Mechanical Engineering,University of Southern California,Los Angeles,CA90089-1453Francisco Alvarez Gonzalez,Dpto.Economia Cuantitativa,Universidad Com-plutense,Madrid,SpainRichard F.Hartl,Institute of Management,University of Vienna,Vienna,Austria Daniel J.Inman,Center for Intelligent Material Systems and Structures,Virginia Polytechnic Institute and State University,Blacksburg,VA24061-0261,USAFernando Kokubun,Department of Physics,Federal University of Rio Grande, Rio Grande,RS,BrazilPeter Kort,Department of Econometrics and Operations Research and CentER, Tilburg University,Tilburg,The NetherlandsG.Leitmann,College of Engineering,University of California,Berkeley CA94720,USAVicente Lopes,Jr.,Department of Mechanical Engineering–UNESP-Ilha Solte-ira,15385-000Ilha Solteira,SP,BrazilS.Mancuso,Rice University,Houston,Texas,USANaor Moraes Melo,Graduate Studies in Mechanical Engineering,Mechanical Engineering Department,Federal University of Paraiba,Campus I,58059-900Joao Pessoa,Paraiba,BrazilLuciano Luporini Menegaldo,S˜a o Paulo State Institute for Technological Re-search,Control System Group/Mechanical and Electrical Engineering Division, P.O.Box0141,CEP01604-970,S˜a o Paulo-SP,BrazilA.Miele,Rice University,Houston,Texas,USAHelio Mitio Morishita,University of S˜a o Paulo,Department of Naval Architec-ture and Ocean Engineering,Av.Prof.Mello Moraes,2231,Cidade Universit´a ria 05508-900,S˜a o Paulo,SP,BrazilFrederico Ricardo Ferreira de Oliveira,Mechanical Engineering Department/ Escola Polit´e cnica,USP–University of S˜a o Paulo,P.O.Box61548,05508-900,S˜a o Paulo,SP,BrazilHumberto Piccoli,Department of Materials Science,Federal University of Rio Grande,Rio Grande,RS,BrazilEduard Reithmeier,Institut f¨u r Meß-und Regelungstechnik,Universit¨a t Han-nover,30167Hannover,GermanyRubens Sampaio,Pontif´ıcia Universidade Cat´o lica do Rio de Janeiro(PUC-Rio), Departamento de Engenharia Mecˆa nica,Rua Marquˆe s de S˜a o Vicente,225,22453-900,G´a vea,Rio de Janeiro,BrasilCopyright © 2004 CRC Press, LLCN.Seube,Ecole Nationale Sup´e rieure des Ing´e nieurs des Etudes et Techniques d’Armement,29806BREST Cedex,FranceMarianna A.Shubov,Department of Mathematics and Statistics,Texas Tech University,Lubbock,TX,79409,USAJo˜a o Morais da Silva Neto,Department of Mechanical Engineering,Federal University of Santa Catarina,BrazilSimplicio Arnaud da Silva,Graduate Studies in Mechanical Engineering,Me-chanical Engineering Department,Federal University of Paraiba,Campus I,58059-900Joao Pessoa,Paraiba,BrazilJess´e Rebello de Souza Junior,University of S˜a o Paulo,Department of Naval Architecture and Ocean Engineering,Av.Prof.Mello Moraes,2231,Cidade Uni-versit´a ria05508-900,S˜a o Paulo,SP,BrazilValder Steffen,Jr.,School of Mechanical Engineering Federal University of Uber-lˆa ndia,38400-902Uberlˆa ndia,MG,BrazilR.Stoop,Institut f¨u r Neuroinformatik,ETHZ/UNIZH,Winterthurerstraße190, CH-8057Z¨u richF.E.Udwadia,Department of Aerospace and Mechanical Engineering,Civil En-gineering,Mathematics,and Operations and Information Management,430K Olin Hall,University of Southern California,Los Angeles,CA90089-1453Vladimir Veliov,Institute for Econometrics,OR and Systems Theory,University of Technology,Argentinierstrasse8,A-1040Vienna,AustriaT.Wang,Rice University,Houston,Texas,USAHans Ingo Weber,DEM-Pontif´ıcia Universidade Cat´o lica–PUC–RJ,CEP 22453-900,Rio de Janeiro,RJ,BrasilCopyright © 2004 CRC Press, LLCPrefaceThis book contains some of the papers that were presented at the11th International Workshop on Dynamics and Control in Rio de Janeiro,October9–11,2000.The workshop brought together scientists and engineers in various diversefields of dy-namics and control and offered a venue for the understanding of this core discipline to numerous areas of engineering and science,as well as economics and biology.It offered researchers the opportunity to gain advantage of specialized techniques and ideas that are well developed in areas different from their ownfields of expertise.This cross-pollination among seemingly disparatefields was a major outcome of this workshop.The remarkable reach of the discipline of dynamics and control is clearly substan-tiated by the range and diversity of papers in this volume.And yet,all the papers share a strong central core and shed understanding on the multiplicity of physical, biological and economic phenomena through lines of reasoning that originate and grow from this discipline.I have separated the papers,for convenience,into three main groups,and thebook is divided into three parts.Thefirst group deals with fundamental advances in dynamics,dynamical systems,and control.These papers represent new ideas that could be applied to several areas of interest.The second deals with new and innovative techniques and their applications to a variety of interesting problems that range across a broad horizon:from the control of cars and robots,to the dynamics of ships and suspension bridges,to the determination of optimal spacecraft trajectories to Mars.The last group of papers relates to social,economic,and biological issues.These papers show the wealth of understanding that can be obtained through a dynamics and control approach when dealing with drug consumption,economic games,epidemics,neo-cortical synchronization,and human posture control.This workshop was funded in part by the US National Science Foundation and CPNq.The organizers are grateful for the support of these agencies.Firdaus E.UdwadiaCopyright © 2004 CRC Press, LLC。