A First-Order Analytical Theory for Optimal Low-Thrust Limited-Power Transfers between Arbitrary Elliptical Coplanar Orbits

Sandro da Silva Fernandes, Francisco das Chagas Carvalho
2008 Mathematical Problems in Engineering  
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
more » ... ciple 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.
doi:10.1155/2008/525930 fatcat:ghujmir47bgwtaw4dme3d4qbym