Multisegment Scheme Applications to Modified Chebyshev Picard Iteration Method for Highly Elliptical Orbits

Abstract EN

A modified Chebyshev Picard iteration method is proposed for solving orbit propagation initial/boundary value problems.

Cosine sampling techniques, known as Chebyshev-Gauss-Lobatto (CGL) nodes, are used to reduce Runge’s phenomenon that plagues many series approximations.

The key benefit of using the CGL data sampling is that the nodal points are distributednonuniformly, with dense sampling at the beginning and ending times.

This problem can be addressedby a nonlinear time transformation and/or by utilizing multiple time segments over anorbit.

This paper suggests a method, called a multisegment method, to obtain accurate solutionsoverall regardless of initial states and albeit eccentricity by dividing the given orbit into two ormore segments based on the true anomaly.