The Jacobi's principle of stationary full action and its consequences

2025/12/14 by V. V. Voytik, Voytik, Vitaliy
Physics and Astronomy · Mathematics · #Advanced Differential Geometry Research #Homotopy and Cohomology in Algebraic Topology #Quantum chaos and dynamical systems

paper · doi:10.48550/arxiv.2512.17944

Abstract

The purpose of this article is to extend the applicability of the stationarity principle of the full Jacobi action to non-conservative natural systems and to derive equations of motion corresponding to this extended principle. To this end, in addition to the well-known variation of the Jacobi action with respect to coordinates, we propose independently variating time. Small variations in coordinates and time depend on the point on the true trajectory with the usual boundary conditions.

Citations

• Real-analyticity of 2-dimensional superintegrable metrics and solution of two Bolsinov-Kozlov-Fomenko conjectures
• Local high-degree polynomial integrals of geodesic flows and the generalized hodograph method
• Trajectory equations for a non-conservative natural system
• Integrable systems on the sphere, ellipsoid and hyperboloid

Related

• Some theorems related to the Jacobi variational principle of analytical dynamics
• The classical mechanics of non-conservative systems
• Jacobi's Action and the Density of States
• Classical Lagrange formalism for non-conservative dynamical systems
• The Principle of Least Action as Interpreted by Nature and by the Observer