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A first-order analytical theory for optimal low-thrust limited-power transfers between arbitrary elliptical coplanar orbits. (English) Zbl 1354.70053

Summary: A complete first-order analytical solution, which includes the short periodic terms, for the problem of optimal low-thrust limited-power transfers between arbitrary elliptic coplanar orbits in a Newtonian central gravity field is obtained through canonical transformation theory. The optimization problem is formulated as a Mayer problem of optimal control theory with Cartesian elements-position and velocity vectors-as state variables. After applying the Pontryagin maximum principle and determining the maximum Hamiltonian, classical orbital elements are introduced through a Mathieu transformation. The short periodic terms are then eliminated from the maximum Hamiltonian through an infinitesimal canonical transformation built through Hori method. Closed-form analytical solutions are obtained for the average canonical system by solving the Hamilton-Jacobi equation through separation of variables technique. For transfers between close orbits a simplified solution is straightforwardly derived by linearizing the new Hamiltonian and the generating function obtained through Hori method.

MSC:

70M20 Orbital mechanics
49K15 Optimality conditions for problems involving ordinary differential equations
49N90 Applications of optimal control and differential games
70F15 Celestial mechanics
70Q05 Control of mechanical systems
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