Nearly-circular periodic solutions of perturbed relativistic Kepler problems: the fixed-period and the fixed-energy problems

2024/05/18 by Alberto Boscaggin, Boscaggin, Alberto, Guglielmo Feltrin +3 · 1 citation
Engineering · Physics and Astronomy · #Spacecraft Dynamics and Control #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2405.11189

Abstract

The paper studies the existence of periodic solutions of a perturbed relativistic Kepler problem of the type \dfracddt(\fracmx√1-|x|²/c²) = -α\fracx|x|³ + ε ∇_x U(t,x), x ∈ ℝ^d∖\0\, with d=2 or d=3, bifurcating, for ε small enough, from the set of circular solutions of the unperturbed system. Both the case of the fixed-period problem (assuming that U is T-periodic in time) and the case of the fixed-energy problem (assuming that U is independent of time) are considered.

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