Celestial mechanics

, Volume 40, Issue 3, pp 315–328

Generalized elliptic anomalies

  • José M. Ferrándiz
  • Sebastián Ferrer
  • María L. Sein-Echaluce
Article

DOI: 10.1007/BF01235849

Cite this article as:
Ferrándiz, J.M., Ferrer, S. & Sein-Echaluce, M.L. Celestial Mechanics (1987) 40: 315. doi:10.1007/BF01235849

Abstract

A two-parameter time transformationdt=r3/201r)−1/2dτ 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.

Copyright information

© D. Reidel Publishing Company 1987

Authors and Affiliations

  • José M. Ferrándiz
    • 1
  • Sebastián Ferrer
    • 2
  • María L. Sein-Echaluce
    • 2
  1. 1.Departmento de Matemática AplicadaE.T.S. Ingenieros IndustrialesValladolidSpain
  2. 2.Departamento de Física TeóricaUniversidad de ZaragozaZaragozaSpain

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