Codimension-4 resonant homoclinic bifurcations with orbit flips and inclination flips

Abstract

The paper studies a codimension-4 resonant homoclinic bifurcation with one orbit flip and two inclination flips, where the resonance takes place in the tangent direction of homoclinic orbit. Local active coordinate system is introduced to construct the Poincaré returning map, and also the associated successor functions. We prove the existence of the saddle-node bifurcation, the perioddoubling bifurcation and the homoclinic-doubling bifurcation, and also locate the corresponding 1-periodic orbit, 1-homoclinic orbit, double periodic orbits and some 2 n -homoclinic orbits.

Circular Orbit Flip Trajectories Generated by E-Sail

“…and the dimensionless time t = t r 3 0 /µ (11) where t 0 = 0 is the initial time. The dimensionless equations of motion are…”

“…Instead, the aim of this paper is to analyze a more specific mission scenario in which the orbital inclination of a given heliocentric Keplerian orbit is changed by exactly 180 degrees. In other terms, this particular plane change maneuver allows the spacecraft to invert its direction of rotation around the Sun, thus obtaining a sort of artificial (thrust-induced) 'orbit flip mechanism' [8][9][10][11], which preserves the shape and the dimension of the original trajectory. More precisely, the focus of this study is on the analysis of the orbit flip mechanism of a circular heliocentric orbit of assigned radius, by means of a two-dimensional propelled trajectory coplanar to the initial circular orbit.…”