mathematica
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(*初始数据*)
m0 = 2.4*10^3;
M = 7.3477*10^22;
G = 6.672*10^-11;
R = 1737.013*10^3;
a = 15*10^3;
b = 359;
e = 2.4*10^3;
c = (100*10^3 + R) - (2 R + 15*10^3 + 100*10^3)/2;
d = (2 R + 15*10^3 + 100*10^3)/2;
g1 = (\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(b\), \(a\)]\(G*
\*FractionBox[\(M\),
SuperscriptBox[\((R + r)\), \(2\)]] \[DifferentialD]r\)\))/(a
- b);
g2 = (\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(e\), \(b\)]\(G*
\*FractionBox[\(M\),
SuperscriptBox[\((R + r)\), \(2\)]] \[DifferentialD]r\)\))/(b
- e);
gave1 == g1(*从15000-395的重力平均加速度*) gave2 == g2(*从3000-2400的重力平均加速度*)
t = 750;(*从vo到0的总时间*)
Va = Sqrt[((d + c)*G*M)/(d*(d - c))];
Vb = Sqrt[((d - c)*G*M)/(d*(c + d))];
vo == Va(*近月点速度*)
l = 600;(*主减速阶段长度*)
m = 1012.68652;(*快速调整阶段的力*)
i = 2940;(*比冲*)
vx2 = \
40.5166740;(*3000时飞船x方向的初速度*)
Vx2 == vx2
vy2 = 40.1809464;(*3000时飞船y方向的初速度*)
Vy2 == vy2
(*求解力*)
ax2 = (f*Sqrt[2]/2.0)/m;
ay2 = ax2 - g2;
t2 = vx2/ax2;
T == t2;
y == vy2*t2 - 0.5*ay2*t2^2; x == vx2*t2 - 0.5*ax2*t2^2;
Solve[-(1/2)*ay2*t2^2 + vy2*t2 == l, f]
F = 3304.255414(*快速调整阶段的力*);
(*最终求解*)
ax2 = (F*Sqrt[2]/2.0)/m;
ay2 = ax2 - g2;
t2 = vx2/ax2;
T == t2
y == vy2*t2 - 0.5*ay2*t2^2;
x == vx2*t2 - 0.5*ax2*t2^2;
vy3 = vy2 - ay2*t2;
Vy3 == vy3
ParametricPlot[{-vx2*t + 0.5*ax2*t^2, -vy2*t + 0.5*ay2*t^2},
{t, 0,
t2}]
(*2400-100，处理方法*)
Clear[m, vy3, g3, L3, F]
Solve[1/2*m*vy3^2 + m*g3*L3 == F*(L3 - x), x]; X[F_] = (2 F L3 - 2 g3 L3 m - m vy3^2)/(2*F);
P[F_] = Sqrt[2*m*F*(L3 - X[F])];
Simplify[%]
(*2400-100，最终求解*)
m = 1011.56262;
L3 = j - k;
g3 = (\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(k\), \(j\)]\(G*
\*FractionBox[\(M\),
SuperscriptBox[\((R + r)\), \(2\)]] \[DifferentialD]r\)\))/(j
- k);
vy3 = vy2 - ay2*t2;
Solve[X[F] == 0, F];
ay3 = 1816.0059/m;
t3 = vy3/ay3;
Dm = 1816.0059/i;
m3 = m - Dm; (*精避障部分*)
SetDirectory[NotebookDirectory[]];
date = Import["a.txt", "Table"];
Clear[i, j]
d0[i_, j_] = Sqrt[(i - 500)^2 + (j - 500)^2];
h[i_, j_] =
1/8*(Abs[date[[i, j]] - date[[i + 1, j]]] +
Abs[date[[i - 1, j]] - date[[i, j]]] +
Abs[date[[i, j + 1]] - date[[i, j]]] +
Abs[date[[i, j]] - date[[i, j - 1]]] +
Abs[date[[i - 1, j + 1]] - date[[i, j]]] +
Abs[date[[i + 1, j + 1]] - date[[i, j]]] +
Abs[date[[i - 1, j - 1]] - date[[i, j]]] +
Abs[date[[i + 1, j - 1]] - date[[i, j]]]);
F[i_, j_] = 0.0079*d0[i, j] + 0.9921*h[i, j];
result = Table[F[i, j], {i, 250, 750}, {j, 250, 750}];
min = Min[result];
p = Position[result, min];
坐标 == p + {{250, 250}}
X4 == d0[528, 327] // N (*100-30，最终求解*)
x4 = 175.251/2;
m4 = 983.459108;
g4 = 1.62626;
m4*g4;
f4 = 1500;
a4 = f4/m4;
i = 2940;
Ax == a4
t4 = 2*Sqrt[2*x4/a4];
T == t4
ay4 = 1299.7898784/m4;
v == (g4 - ay4)*t4
F4 = Sqrt[1299.789878421^2 + f4^2];
Dm4 = F4/i*t4;
M4 = m4 - Dm4
vy40 = (g4 - ay4)*t4/2;
vx40 = a4*t4/2;
gr1 = Table[{x, -((g4 - ay4)/a4)*x + 100}, {x, 0, 87.6225,
0.5}];
gr2 = Table[{vx40*ts - 1/2*a4*ts^2 + 87.6225, -vy40*ts - 1/2*(g4 - ay4)*ts^2 + 82.4926}, {ts, 0, t4/2, 0.1}];
ListLinePlot[{gr1, gr2}]
(*30-4，最终求解*)
v5 = (g4 - ay4)*t4;
x5 = 26;
a5 = v5^2/(2*x5);
F5 = (g4 + a5)*M4
t5 = v5/a5
Dm5 = F5/i*t5;
M4 - Dm5
