The Lagrangian theory of Staeckel Systems

Details The Lagrangian theory of Staeckel Systems The Lagrangian theory of Staeckel Systems

Oct 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981cemec..25..185b&link_type=abstract

Celestial Mechanics, vol. 25, Oct. 1981, p.185-193.

Mathematics

1

Astrodynamics, Celestial Mechanics, Degrees Of Freedom, Equations Of Motion, Euler-Lagrange Equation, Canonical Forms, Determinants, Hamilton-Jacobi Equation, Kepler Laws, Matrices (Mathematics), Orbital Mechanics, Transformations (Mathematics), Vector Analysis

Scientific paper

A purely Lagrangian formulation and a direct proof of the separation of variables theorem is given for what is called Staeckel Systems in dynamics and celestial mechanics. The proof is essentially based on some properties of determinants and minors (given in Appendix A). In contrast with the standard literature on the subject, the use of the Hamiltonian, canonical transformations or the Hamilton-Jacobi equation is avoided by using instead a more elementary approach based on the Lagrangian. In Appendix B we use the Kepler Problem as an illustration of the Lagrangian theory of Staeckel Systems.

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