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?

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

1 Answer 1


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


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.