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Numerical and analytical study of optimal low-thrust limited-power transfers between close circular coplanar orbits. (English) Zbl 1360.70037

Summary: A numerical and analytical study of optimal low-thrust limited-power trajectories for simple transfer (no rendezvous) between close circular coplanar orbits in an inverse-square force field is presented. The numerical study is carried out by means of an indirect approach of the optimization problem in which the two-point boundary value problem, obtained from the set of necessary conditions describing the optimal solutions, is solved through a neighboring extremal algorithm based on the solution of the linearized two-point boundary value problem through Riccati transformation. The analytical study is provided by a linear theory which is expressed in terms of nonsingular elements and is determined through the canonical transformation theory. The fuel consumption is taken as the performance criterion and the analysis is carried out considering various radius ratios and transfer durations. The results are compared to the ones provided by a numerical method based on gradient techniques.

MSC:

70M20 Orbital mechanics
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
49K15 Optimality conditions for problems involving ordinary differential equations
49M05 Numerical methods based on necessary conditions
70Q05 Control of mechanical systems
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