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For the Earth Moon transfer trajectory, analytical and numerical methods are combined to formulate the trajectory optimization problem.
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The conventional patched conic method, the most widely used analytical trajectory design method, does not identify these design options.
An iterative analytical trajectory design technique that includes perturbations in the departure phase of the interplanetary orbiter missions is proposed.
Analytical trajectories are therefore useful aids in a preliminary phase of mission design, even though exact solution are very difficult to obtain.
As seen in Fig. 2 with K A = 50, trajectories from ODEs, analytical approximations, and stochastic simulations are quite similar.
However, it has been unclear how dependent these trajectories are on the analytical model used and the pain characteristics included.
A control law providing motion of the vehicles along smooth and composite analytical curves (trajectories) is designed.
Furthermore, the recursive equations describing the propagation trajectory are formulated and the analytical result of the propagation trajectory is in good agreement with the numerical one.
Now, the numerical program for ray tracing simulations was written, fully basing on our original analytical calculation of trajectories.
For the analytical and ODE trajectories, the only difference is a 50× scaling in the output amplitudes.
The requirement of high-latitude landing for the return phase trajectory is considered in the modified analytical model.
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