A Lagrangian formulation for changing MacGehee variables, in polar coordinates

Details A Lagrangian formulation for changing MacGehee variables, in polar coordinates A Lagrangian formulation for changing MacGehee variables, in polar coordinates

Nov 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984crasb.299..933n&link_type=abstract

Academie des Sciences (Paris), Comptes Rendus, Serie II Mecanique, Physique, Chimie, Sciences de l'Univers, Sciences de la Terre

Physics

Celestial Mechanics, Euler-Lagrange Equation, Three Body Problem, Kepler Laws, Rotating Bodies

Scientific paper

A double change of variable is considered for modeling the motions of three aligned bodies, a system usually treated with MacGehee (1974) equations for a triple collision. A Lagrangian formulation is found for the sum of the forces of the three bodies. The MacGehee formulation is shown to be a special case of the Lagrangian expression, as is the Sundman three-body problem. Two sample calculations are carried out, the Keplerian problem of the rotation of a solid body around its center of gravity and the three body problem. Stability conditions are discussed for the latter problem.

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