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I need to solve a boundary value problem (BVP) for an optimal control in case of low thrust trajectories optimization. I want to include the J2 perturbations to the Edelbaum solution (multiple revolutions one).

In my specific case I am:

  • capable to define the state equations, for semi-major-axis, inclination, raan and mass

  • capable to define the Euler Lagrange equations for the adjoint parameters (lambdas entering the Hemiltonian formula)

  • capable to set general boundary conditions

However, I can't understand how to integrate in time, since time is not present as a variable inside the equations and how to initialize the problem: setting values for OP and adjoint variables.

Furthermore I am looking for some tools automatically implementing and solving this problems automatically (better if written in Python), anyone know something about that?

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  • $\begingroup$ OP = ? Please provide a link for the J2 perturbations and the Edelbaum solution. $\endgroup$
    – Rodrigo de Azevedo
    Commented Sep 18, 2022 at 13:21
  • $\begingroup$ If you mention the optimal numerical method, you must provide a cost function. $\endgroup$
    – Rodrigo de Azevedo
    Commented Sep 18, 2022 at 13:21
  • $\begingroup$ OP stands for Orbital Parameters $\endgroup$
    – Pietro De Marchi
    Commented Sep 19, 2022 at 9:18
  • $\begingroup$ I read OP = "optimization problem". $\endgroup$
    – Rodrigo de Azevedo
    Commented Sep 19, 2022 at 9:36

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ESA's PyKep will likely work very well. It allows you to solve lots of BVP, model low thrust propulsion, load SPICE files, etc.

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