Direct lunar descent optimisation by finite elements in time approach

In this paper a direct approach to trajectory optimisation, based on Finite Elements in Time (FET) discretisation is presented. Trajectory optimisation is performed combining the effectiveness and flexibility of Finite Elements in Time in solving complex boundary values problems with a common nonlinear programming algorithm. In order to avoid low accuracy proper to direct approaches, a mesh adaptivity strategy is implemented which exploits the ability of finite elements to represent both continuous and discontinuous functions. The effectiveness and accuracy of direct transcription by FET are proved by a selected number of sample problems. Finally an optimal landing manoeuvre is presented to show the power of the proposed approach in solving even complex and realistic problems

Numerical solutions for lunar orbits

Starting from a variational formulation based on Hamilton’s Principle, the paper exploits the finite element technique in the time domain in order to solve orbital dynamic problems characterised by constrained boundary value rather than initial value problems. The solution is obtained assembling a suitable number of finite elements inside the time interval of interest, imposing the desired constraints, and solving the resultant set of non-linear algebraic equations by means of Newton-Raphson method. In particular, in this work this general solution strategy is applied to periodic orbits determination. The effectiveness of the approach in finding periodic orbits in the unhomogeneous gravity field of the Moon is assessed by means of relevant examples, and the results are compared with those obtained by standard time marching techniques as well as with analytical results