About the Constant of Motion, Lagrangian and Hamiltonian of the Gravitational Attraction of Two Bodies with Variable Mass (Gylden-Meshcherskii problem)

2007/03/06 by Gustavo V. López, G. Lopez, Lopez, G. +2
Engineering · Physics and Astronomy · #Classical Physics (physics.class-ph) #FOS: Physical sciences #General Physics (physics.gen-ph) #Material Science and Thermodynamics #Relativity and Gravitational Theory #physics.class-ph #physics.gen-ph

paper · pdf · doi:10.48550/arxiv.physics/0703071

11 pages and 2 figures

arxiv created 2007/03/06 · openalex publication_date 2007/03/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Lagrangian, the Hamiltonian and the constant of motion of the gravitational attraction of two bodies when one of them has variable mass is considered. This is done by choosing the reference system in one of the bodies which allows to reduce the system of equations to 1-D problem. The trajectories found in the space position-velocity,(x,v), are qualitatively different from those on the space position-momentum,(x,p).

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