Generalized elliptic anomalies

A two-parameter time transformationdt=r ^3/2(α₀+α₁ 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.