On tensor invariants of the Clebsch system

2025/04/21 by Tsiganov, A. V. · 2 citations
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2504.14867

Abstract

We present some new Poisson bivectors that are invariants by the Clebsch system flow. Symplectic integrators on their symplectic leaves exactly preserve the corresponding Casimir functions, which have different physical meanings. The Kahan discretization of the Clebsch system is discussed briefly.

Cited by

• Homogeneous potentials, Lagrange's identity and Poisson geometry
• On novel Hamiltonian description of the nonholonomic Suslov problem

Related

• A Class of Integrable Geodesic Flows on the Symplectic Group and the Symmetric Matrices
• The Clebsch System
• On novel Hamiltonian description of the nonholonomic Suslov problem
• On the Liouville-Arnold integrable flows related with quantum algebras and their Poissonian representations
• Poisson structures of some heavenly type dynamical systems