Optimization of Low-Thrust Limited-Power Trajectories in a Noncentral Gravity Field—Transfers between Orbits with Small Eccentricities

Sandro da Silva Fernandes

Mathematical Problems in Engineering, 2009, vol. 2009, 1-35

Abstract:

Numerical and first-order analytical results are presented for optimal low-thrust limited-power trajectories in a gravity field that includes the second zonal harmonic ð ½ 2 in the gravitational potential. Only transfers between orbits with small eccentricities are considered. The optimization problem is formulated as a Mayer problem of optimal control with Cartesian elements—position and velocity vectors—as state variables. After applying the Pontryagin Maximum Principle, successive canonical transformations are performed and a suitable set of orbital elements is introduced. Hori method—a perturbation technique based on Lie series—is applied in solving the canonical system of differential equations that governs the optimal trajectories. First-order analytical solutions are presented for transfers between close orbits, and a numerical solution is obtained for transfers between arbitrary orbits by solving the two-point boundary value problem described by averaged maximum Hamiltonian, expressed in nonsingular elements, through a shooting method. A comparison between analytical and numerical results is presented for some maneuvers.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:503168

DOI: 10.1155/2009/503168

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