, Volume 40, Issue 3-4, pp 315-328

Generalized elliptic anomalies

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Abstract

A two-parameter time transformationdt=r 3/201 r)−1/2 dτ is proposed, where τ is the radial distance while α0 and α1 are, if not constants, at least conservative functions of positions and velocities. In Keplerian systems, the quadrature implied by the transformation may by carried out by elliptic functions. When α0=0, τ is the eccentric anomaly; if α1=0, then τ is the intermediate or elliptic anomaly. Considering several values of α0 and α1, numerical examples of the relation of thegeneralized elliptic anomaly τ with the classical and elliptic anomalies are given. Application of this transformation to some perturbed Kepler problems is briefly outlined.