Lie-point symmetries of the Lagrangian system on time scales

2012/12/11 by Ping-ping Cai, Ping-Ping, Cai, Song-Duan +4
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Numerical methods for differential equations #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.1212.2361

openalex publication_date 2012/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This letter investigates the Lie point symmetries and conserved quantities of the Lagrangian systems on time scales, which unify the Lie symmetries of the two cases for the continuous and the discrete Lagrangian systems. By defining the infinitesimal transformations' generators and using the invariance of differential equations under infinitesimal transformations, the determining equations of the Lie symmetries on time scales are established. Then the structure equations and the form of conserved quantities with delta derivatives are obtained. The letter also gives brief discussion on the Lie symmetries for the discrete systems. Finally, several examples are designed to illustrate these results.

Related

• Lie symmetries, Jacobi last multipliers and new non-standard Lagrangians for dissipative dynamical systems
• Lambda-symmetries of Dynamical Systems, Hamiltonian and Lagrangian equations
• The commutativity principle and lagrangian symmetries
• Estimating quantities conserved by virtue of scale invariance in timeseries
• On the Lie symmetries of Kepler-Ermakov systems