Dynamics cheat sheet

Algorithm 3 Hohmann rendezvous algorithm, case 2
1: function hohmann rendezvous 2(θ 0 , r 1 , r 2 , N, µ)
π
2: θ 0 := θ 0 180 (
⊲ convert from degrees to radian
( ) ) 3/2
3: θ H := π 1 − r1 +r 2
2r 2
⊲ Find Hohmann ideal phase angle before transfer
4: if θ 0 = θ H and N = 0 then ⊲ adjust for special case
5: a := r 2+r 1
2 (√
6: TOF := π
)
a 3
µ
7: else
8: ω 2 := √ µ
r2
3
9: t 2 := (2π−θ 0)+2πN
ω 2
10: a 1 := rt+r 1
2
11: a 2 := rt+r 2
2
12: TOF := π
(√
a 3
1
µ
+ a3 2
µ
)
⊲ angular speed of slower satellite in rad/sec
⊲ find time of light of the slower satellite
⊲ time of flight for the fast satellite
13: r t := solve (t 2 = T OF ) for r t ⊲ Solve numerically for r t
14: end if
15: return TOF
16: end function
An example implementation is below
1 hohmann_rendezvous_2:= proc({
2 theta::numeric:=0,
3 r1::numeric:=0,
4 r2::numeric:=0,
5 N::nonnegint:=0,
6 mu::numeric:=3.986*10^5})
7 local theta0,thetaH,TOF;
8 theta0 := theta*Pi/180;
9 thetaH := Pi*(1-((r1+r2)/(2*r2))^(3/2));
10 if theta0 = thetaH and N = 0 then
11 proc()
12 local a:=(r1+r2)/2;
13 TOF:= Pi*(sqrt(a^3/mu));
14 end proc()
15 else
16 proc()
17 local t2,a1,a2,rt,omega2;
18 omega2 := sqrt(mu/r2^3);
19 t2 := ((2*Pi-theta0)+2*Pi*N)/omega2;
20 a1 := (rt+r1)/2;
21 a2 := (rt+r2)/2;
22 TOF := Pi*(sqrt(a1^3/mu)+sqrt(a2^3/mu));
23 rt := op(select(is, [solve(t2=TOF,rt)], real));
24 end proc()
25 fi;
26 eval(TOF);
27 end proc:
And calling the above for two different cases gives
86