# Multi-Revolution Low-Thrust Trajectory Optimization Using Symplectic Methods. (arXiv:1901.02881v1 [physics.space-ph])

Multi-Revolution Low-Thrust Trajectory Optimization Using Symplectic Methods. (arXiv:1901.02881v1 [physics.space-ph])
<a href="http://arxiv.org/find/physics/1/au:+E_Z/0/1/0/all/0/1">Zhibo E</a>, <a href="http://arxiv.org/find/physics/1/au:+Guzzetti_D/0/1/0/all/0/1">Davide Guzzetti</a>

Optimization of low-thrust trajectories that involve a larger number of orbit
revolutions is considered a challenging problem. This paper describes a
high-precision symplectic method and optimization techniques to solve the
minimum-energy low-thrust multi-revolution orbit transfer problem. First, the
optimal orbit transfer problem is posed as a constrained nonlinear optimal
control problem. Then, the constrained nonlinear optimal control problem is
converted into an equivalent linear quadratic form near a reference solution.
The reference solution is updated iteratively by solving a sequence of
linear-quadratic optimal control sub-problems, until convergence. Each
sub-problem is solved via a symplectic method in discrete form. To facilitate
the convergence of the algorithm, the spacecraft dynamics are expressed via
modified equinoctial elements. Interpolating the non-singular equinoctial
orbital elements and the spacecraft mass between the initial point and end
point is proven beneficial to accelerate the convergence process. Numerical
examples reveal that the proposed method displays high accuracy and efficiency.

Optimization of low-thrust trajectories that involve a larger number of orbit
revolutions is considered a challenging problem. This paper describes a
high-precision symplectic method and optimization techniques to solve the
minimum-energy low-thrust multi-revolution orbit transfer problem. First, the
optimal orbit transfer problem is posed as a constrained nonlinear optimal
control problem. Then, the constrained nonlinear optimal control problem is
converted into an equivalent linear quadratic form near a reference solution.
The reference solution is updated iteratively by solving a sequence of
linear-quadratic optimal control sub-problems, until convergence. Each
sub-problem is solved via a symplectic method in discrete form. To facilitate
the convergence of the algorithm, the spacecraft dynamics are expressed via
modified equinoctial elements. Interpolating the non-singular equinoctial
orbital elements and the spacecraft mass between the initial point and end
point is proven beneficial to accelerate the convergence process. Numerical
examples reveal that the proposed method displays high accuracy and efficiency.

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