Improved semi-analytical computation of center manifolds near collinear libration points

Abstract

In the framework of the circular restricted three-body problem, the center manifolds associated with collinear libration points contain all the bounded orbits moving around these points. Semi-analytical computation of the center manifolds and the associated canonical transformation are valuable tools for exploring the design space of libration point missions. This paper deals with the refinement of reduction to the center manifold procedure. In order to reduce the amount of calculation needed and avoid repetitive computation of the Poisson bracket, a modified method is presented. By using a polynomial optimization technique, the coordinate transformation is conducted more efficiently. In addition, an alternative way to do the canonical coordinate transformation is discussed, which complements the classical approach. Numerical simulation confirms that more accurate and efficient numerical exploration of the center manifold is made possible by using the refined method.