Optimization of Low-Thrust Limited-Power Trajectories in a Noncentral Gravity Field—Transfers between Orbits with Small Eccentricities. (19th July 2009)

• Record Type: Journal Article
• Authors: da Silva Fernandes, Sandro
• Other Names: Quinn Dane Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2009(2009)
• Publication Date: 2009-07-19
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2009/503168
• Languages: English
• ISSNs: 1024-123X

Abstract

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 J 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.