Energy-conserving methods for Hamiltonian Boundary Value Problems and applications in astrodynamics

TL;DR

This paper presents energy-conserving numerical methods for Hamiltonian boundary value problems, enabling precise energy preservation in solutions and applications in astrodynamics such as finding periodic orbits and optimal transfers.

Contribution

The paper introduces novel energy-conserving numerical methods specifically designed for Hamiltonian boundary value problems, with applications in astrodynamics.

Findings

Methods precisely conserve energy in numerical solutions.

Successful application to locate periodic orbits in the three-body problem.

Effective in solving optimal transfer problems in astrodynamics.

Abstract

We introduce new methods for the numerical solution of general Hamiltonian boundary value problems. The main feature of the new formulae is to produce numerical solutions along which the energy is precisely conserved, as is the case with the analytical solution. We apply the methods to locate periodic orbits in the circular restricted three body problem by using their energy value rather than their pe- riod as input data. We also use the methods for solving optimal transfer problems in astrodynamics.