Abstract
Two-point boundary value problems appear frequently in space trajectory design. A remarkable example is represented by the Lambert’s problem, where the conic arc linking two fixed positions in space in a given time is to be characterized in the frame of the two- body problem. However, a certain level of approximation always affects the dynamical models adopted to design the nominal trajectory of a spacecraft. Dynamical perturbations usually act on the spacecraft in real scenarios, deviating it from the desired nominal trajectory. Conse- quently, the boundary conditions assumed for the nominal solutions are usually affected by uncertainties and errors. Suitable techniques must be developed to quickly compute correction maneuvers to compensate for such errors in practical applications. This work proposes differential algebra as a valuable tool to face the previous problem. An algorithm is presented, which is able to deliver the arbitrary order Taylor expansion of the solution of a two-point boundary value problem about an available nominal solution. The mere evaluation of the resulting polynomials en- ables the design of the desired correction maneuvers. The performances of the algorithm are assessed by addressing typical applications in the field of spacecraft dynamics, such as the simple Lambert’s problem and the station keeping of a spacecraft around a nominal halo orbit.