Constant of motion, Lagrangian and Hamiltonian of the gravitational attraction of two bodies with variable mass

Details Constant of motion, Lagrangian and Hamiltonian of the gravitational attraction of two bodies with variable mass Constant of motion, Lagrangian and Hamiltonian of the gravitational attraction of two bodies with variable mass

2005-11-09

arxiv.org/abs/physics/0511086v1

Physics

Classical Physics

11 pages, 3 figures, sent to IJMP

Scientific paper

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. The relative and center of mass coordinates are not separated, and choosing the reference system in the body with much higher mass, it is possible to reduce the system of equations to 1-D problem. Then, a constant of motion, the Lagrangian, and the Hamiltonian are obtained. 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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