Unified Symbolic Algorithm for Some Expansions of the Two-Body Problem Using Lagrange’s Fundamental Invariants

In this paper, four symbolic computing algorithms are developedfor time series expansions of the following two-body problem:the lagrange f and g functions, radial distance, the normalizedinner product of the position and velocity vectors, and the eccentricanomaly of elliptic motion. to obtain these expansions once and forall, we proposed a unified approach in which lagrange.s fundamentalinvariants were used to develop time series solution of single harmonicoscillator equation.