Es wäre vor allem die Frage, wo man dann die Vorzeichen umkehren sollte, damit man mit der Realität in Einklang stehende Ergebnisse erhält.
Anziehung:
Code:
x1'[t] == vx1[t], y1'[t] == vy1[t], z1'[t] == vz1[t],
x2'[t] == vx2[t], y2'[t] == vy2[t], z2'[t] == vz2[t],
x3'[t] == vx3[t], y3'[t] == vy3[t], z3'[t] == vz3[t],
x4'[t] == vx4[t], y4'[t] == vy4[t], z4'[t] == vz4[t],
vx1'[t] == (G m2 (x2[t] - x1[t]))/
Sqrt[((x2[t] - x1[t])^2 + (y2[t] - y1[t])^2 + (z2[t] -
z1[t])^2)^3] + (G m3 (x3[t] - x1[t]))/
Sqrt[((x3[t] - x1[t])^2 + (y3[t] - y1[t])^2 + (z3[t] -
z1[t])^2)^3] + (G m4 (x4[t] - x1[t]))/
Sqrt[((x4[t] - x1[t])^2 + (y4[t] - y1[t])^2 + (z4[t] - z1[t])^2)^3],
vy1'[t] == (G m2 (y2[t] - y1[t]))/
Sqrt[((x2[t] - x1[t])^2 + (y2[t] - y1[t])^2 + (z2[t] -
z1[t])^2)^3] + (G m3 (y3[t] - y1[t]))/
Sqrt[((x3[t] - x1[t])^2 + (y3[t] - y1[t])^2 + (z3[t] -
z1[t])^2)^3] + (G m4 (y4[t] - y1[t]))/
Sqrt[((x4[t] - x1[t])^2 + (y4[t] - y1[t])^2 + (z4[t] - z1[t])^2)^3],
vz1'[t] == (G m2 (z2[t] - z1[t]))/
Sqrt[((x2[t] - x1[t])^2 + (y2[t] - y1[t])^2 + (z2[t] -
z1[t])^2)^3] + (G m3 (z3[t] - z1[t]))/
Sqrt[((x3[t] - x1[t])^2 + (y3[t] - y1[t])^2 + (z3[t] -
z1[t])^2)^3] + (G m4 (z4[t] - z1[t]))/
Sqrt[((x4[t] - x1[t])^2 + (y4[t] - y1[t])^2 + (z4[t] - z1[t])^2)^3],
vx2'[t] == (G m1 (x1[t] - x2[t]))/
Sqrt[((x1[t] - x2[t])^2 + (y1[t] - y2[t])^2 + (z1[t] -
z2[t])^2)^3] + (G m3 (x3[t] - x2[t]))/
Sqrt[((x3[t] - x2[t])^2 + (y3[t] - y2[t])^2 + (z3[t] -
z2[t])^2)^3] + (G m4 (x4[t] - x2[t]))/
Sqrt[((x4[t] - x2[t])^2 + (y4[t] - y2[t])^2 + (z4[t] - z2[t])^2)^3],
vy2'[t] == (G m1 (y1[t] - y2[t]))/
Sqrt[((x1[t] - x2[t])^2 + (y1[t] - y2[t])^2 + (z1[t] -
z2[t])^2)^3] + (G m3 (y3[t] - y2[t]))/
Sqrt[((x3[t] - x2[t])^2 + (y3[t] - y2[t])^2 + (z3[t] -
z2[t])^2)^3] + (G m4 (y4[t] - y2[t]))/
Sqrt[((x4[t] - x2[t])^2 + (y4[t] - y2[t])^2 + (z4[t] - z2[t])^2)^3],
vz2'[t] == (G m1 (z1[t] - z2[t]))/
Sqrt[((x2[t] - x1[t])^2 + (y2[t] - y1[t])^2 + (z2[t] -
z1[t])^2)^3] + (G m3 (z3[t] - z2[t]))/
Sqrt[((x3[t] - x2[t])^2 + (y3[t] - y2[t])^2 + (z3[t] -
z2[t])^2)^3] + (G m4 (z4[t] - z2[t]))/
Sqrt[((x4[t] - x2[t])^2 + (y4[t] - y2[t])^2 + (z4[t] - z2[t])^2)^3],
vx3'[t] == (G m1 (x1[t] - x3[t]))/
Sqrt[((x1[t] - x3[t])^2 + (y1[t] - y3[t])^2 + (z1[t] -
z3[t])^2)^3] + (G m2 (x2[t] - x3[t]))/
Sqrt[((x2[t] - x3[t])^2 + (y2[t] - y3[t])^2 + (z2[t] -
z3[t])^2)^3] + (G m4 (x4[t] - x3[t]))/
Sqrt[((x4[t] - x3[t])^2 + (y4[t] - y3[t])^2 + (z4[t] - z3[t])^2)^3],
vy3'[t] == (G m1 (y1[t] - y3[t]))/
Sqrt[((x1[t] - x3[t])^2 + (y1[t] - y3[t])^2 + (z1[t] -
z3[t])^2)^3] + (G m2 (y2[t] - y3[t]))/
Sqrt[((x2[t] - x3[t])^2 + (y2[t] - y3[t])^2 + (z2[t] -
z3[t])^2)^3] + (G m4 (y4[t] - y3[t]))/
Sqrt[((x4[t] - x3[t])^2 + (y4[t] - y3[t])^2 + (z4[t] - z3[t])^2)^3],
vz3'[t] == (G m1 (z1[t] - z3[t]))/
Sqrt[((x1[t] - x3[t])^2 + (y1[t] - y3[t])^2 + (z1[t] -
z3[t])^2)^3] + (G m2 (z2[t] - z3[t]))/
Sqrt[((x2[t] - x3[t])^2 + (y2[t] - y3[t])^2 + (z2[t] -
z3[t])^2)^3] + (G m4 (z4[t] - z3[t]))/
Sqrt[((x4[t] - x3[t])^2 + (y4[t] - y3[t])^2 + (z4[t] - z3[t])^2)^3],
vx4'[t] == (G m1 (x1[t] - x4[t]))/
Sqrt[((x1[t] - x4[t])^2 + (y1[t] - y4[t])^2 + (z1[t] -
z4[t])^2)^3] + (G m2 (x2[t] - x4[t]))/
Sqrt[((x2[t] - x4[t])^2 + (y2[t] - y4[t])^2 + (z2[t] -
z4[t])^2)^3] + (G m3 (x3[t] - x4[t]))/
Sqrt[((x3[t] - x4[t])^2 + (y3[t] - y4[t])^2 + (z3[t] - z4[t])^2)^3],
vy4'[t] == (G m1 (y1[t] - y4[t]))/
Sqrt[((x1[t] - x4[t])^2 + (y1[t] - y4[t])^2 + (z1[t] -
z4[t])^2)^3] + (G m2 (y2[t] - y4[t]))/
Sqrt[((x2[t] - x4[t])^2 + (y2[t] - y4[t])^2 + (z2[t] -
z4[t])^2)^3] + (G m3 (y3[t] - y4[t]))/
Sqrt[((x3[t] - x4[t])^2 + (y3[t] - y4[t])^2 + (z3[t] - z4[t])^2)^3],
vz4'[t] == (G m1 (z1[t] - z4[t]))/
Sqrt[((x1[t] - x4[t])^2 + (y1[t] - y4[t])^2 + (z1[t] -
z4[t])^2)^3] + (G m2 (z2[t] - z4[t]))/
Sqrt[((x2[t] - x4[t])^2 + (y2[t] - y4[t])^2 + (z2[t] -
z4[t])^2)^3] + (G m3 (z3[t] - z4[t]))/
Sqrt[((x3[t] - x4[t])^2 + (y3[t] - y4[t])^2 + (z3[t] - z4[t])^2)^3],
... http://yukterez.ist.org/3kp
Abstoßung:
Code:
?
Neugierig, Yukterez