Asymptotic stabilisation of motion on circular intermediate thrust arcs in a field of two fixed centres

The variational problem of minimising the characteristic velocity of motion in a gravitational field of two fixed centres is considered. It is shown that if a cylindrical coordinate system with the origin at one of the fixed centres is introduced, then the differential equations of motion on circular intermediate thrust arcs are analytically integrable using the method of Levi-Civita and particular analytical solutions can be formulated. The controllability at the first approximation and asymptotic stability of an unperturbed motion on such arcs can be achieved by changing only the transversal component of the thrust vector. Illustrative example is presented.

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