A new understanding of L4 and L5 axial orbits through the torus structure

Abstract

ABSTRACT In this paper, through the critical isosurface of the pseudo-Hamiltonian of co-orbital motions in the torus space, we provide a new understanding of L4 and L5 axial orbits and their invariant manifolds in the circular restricted three-body problem. The contact points on the critical isosurface of the pseudo-Hamiltonian correspond to the locations of L4 and L5 axial orbits in the torus space, and provide a set of good initial guesses of L4 and L5 axial orbits for the multiple shooting method. Furthermore, we calculate and analyse orbital behaviours of L4 and L5 axial orbit families. Based on the topological structure of the critical isosurface of the pseudo-Hamiltonian, compound dynamical motions of invariant manifolds associated with L4 and L5 axial orbits are discussed. We present an approximate estimation for libration amplitudes of different co-orbital portions of invariant manifolds. Results obtained from numerical integration demonstrate the validity of our semi-analytical approach in the torus space..