AAS 98-126

HARMONIC OSCILLATOR SOLUTIONS TO LINEARIZABLE PERTURBATIONS OF TWO-BODY PROBLEMS

I. Aparicio, L. Floria - Universidad de Valladolid, Spain

Abstract

In extended phase-space formulation, we analyze the exact linearization (say, reduction to second-order differential equations with constant coefficients governing a set of harmonic oscillators) of the equations of motion derived from a class of perturbed Keplerian Hamiltonian systems, and solve the resulting set of second-order equations. The said exact linearization is studied in terms of the so-called BF-, DEF- and D-variables, originally devised to regularize and exactly linearize unperturbed Keplerian Hamiltonian systems. We characterize perturbing potentials admitting exact linearization in these variables, and obtain the respective solutions corresponding to harmonic oscillators.

Back