Separation of variables in Hamilton–Jacobi equation for a charged test particle in the Stackel spaces of type (2.1)

2020/08/31 by Valeriy Obukhov
Engineering · Physics and Astronomy · #Equations of motion #Equivalence (formal languages) #Geophysics and Sensor Technology #Motion (physics) #Particle (ecology) #Quantum Mechanics and Non-Hermitian Physics #Quantum and Classical Electrodynamics #Separation (statistics) #Separation of variables #Test particle #Type (biology) #gr-qc #msc:83C10 #msc:83C15 #msc:83C20 #msc:83C50

paper · pdf · doi:10.1142/s0219887820501868

published as International Journal of Geometric Methods in Modern Physics Vol. 17, No. 14 (2020) 2050186 (20 pages)

openalex publication_date 2020/08/31 · openalex created_date 2020/09/01 · arxiv created 2020/12/11 · arxiv updated 2020/12/14 · openalex updated_date 2026/08/05

Abstract

We can find all equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces, provided that the equations of motion of the classical charged test particles are integrated by the method of complete separation of variables in the Hamilton–Jacobi equation. Separation is carried out using the complete sets of mutually-commuting integrals of motion of type (2.1), whereby in a privileged coordinate system the Hamilton–Jacobi equation turns into a parabolic type equation.

Citations

• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests
• Sulla integrazione della equazione di Hamilton-Jacobi per separazione di variabili

Cited by

• Hamilton–Jacobi Equation for a Charged Test Particle in the Stäckel Space of Type (2.0)