Optimal low-thrust rendezvous using equinoctial orbit elements

Abstract

The problem of optimal low-thrust rendezvous using continuous constant acceleration is presented based on the use of the non-singular equinoctial orbit elements. State and adjoint equations are integrated numerically by applying the thrust vector along a direction that maximizes the variational Hamiltonian at each instant of time. The two-point-boundary-value problem is solved via a Newton-Raphson scheme after guessing the initial values of the Lagrange multipliers as well as the total flight time. The transversality condition for the Hamiltonian at the final time is also used to carry out the 7 × 7 search. Equinoctial elements have previously been used to carry out minimum-time orbit transfers by considering only the five slowly varying elements. The inclusion of the sixth element representing the fast variable has allowed us to extend the applicability of the non-singular formulation to problems of orbital rendezvous.