Control of chaos in the vicinity of the Earth--Moon L5 Lagrangian point to keep a spacecraft in orbit

TL;DR

This paper introduces a novel control method combining Space Manifold Dynamics and the OGY method to stabilize spacecraft near the Earth--Moon L5 Lagrangian point, demonstrating effective orbit-keeping in complex gravitational models.

Contribution

It develops a modified OGY control approach with a time-dependent force to maintain spacecraft near L5, integrating phase space mapping and trajectory stabilization techniques.

Findings

Successfully kept a spacecraft near L5 using the control method

Determined optimal control parameters through numerical experiments

Mapped phase space around L5 for better orbit prediction

Abstract

The concept of Space Manifold Dynamics is a new method of space research. We have applied it along with the basic idea of the method of Ott, Grebogi and York (OGY method) to stabilize the motion of a spacecraft around the triangular Lagrange point L5 of the Earth--Moon system. We have determined the escape rate of the trajectories in the general three- and four-body problem and estimated the average lifetime of the particles. Integrating the two models we mapped in detail the phase space around the L5 point of the Earth--Moon system. Using the phase space portrait our next goal was to apply a modified OGY method to keep a spacecraft close to the vicinity of L5. We modified the equation of motions with the addition of a time dependent force to the motion of the spacecraft. In our orbit--keeping procedure there are three free parameters: (i) the magnitude of the thrust, (ii) the start time and (iii) the length of the control. Based on our numerical experiments we were able to determine possible values for these parameters and successfully apply a control phase to a spacecraft to keep it on orbit around L5.