Unified symbolic algorithm for some expansions of the two-body problem using lagranges fundamental invariants

Abstract EN

In this paper, four symbolic computing algorithms are developed for time series expansions of the following two-body problem: The Lagrange f and g functions, radial distance, the normalized inner product of the position and velocity vectors, and the eccentric anomaly of elliptic motion.

To obtain these expansions once and for all, we proposed a unified approach in which Lagrange is fundamental invariants were used to develop time series solution of single harmonic oscillator equation.