Some theorems related to the Jacobi variational principle of analytical dynamics

2005/03/30 by Stanisław L. Bażański, Bażański, Stanisław L.
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Pulsars and Gravitational Waves Research #Quantum chaos and dynamical systems #gr-qc #math-ph #math.MP #msc:53B30. #msc:53B50 #msc:70H30 #msc:83-02 #msc:83C20

paper · pdf · doi:10.48550/arxiv.math-ph/0503072

Submitted to a prepared volume in celebration of 75-th birthday of Jerzy Plebanski

arxiv created 2005/03/30 · arxiv updated 2009/12/01

Abstract

It is shown that there exists a commuting diagram of mappings between dynamics of classical systems on one side and variational principles for geodesic lines in stationary spacetimes of general relativity on the other. The construction of the mappings is based on classical Routh's and Jacobi's procedures and on corresponding inverse procedures which are reviewed in the paper.

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