Decomposing Euler–Poincaré Flow on the Space of Hamiltonian Vector Fields
Abstract
:1. Introduction
2. Coupling of Euler–Poincaré Dynamics
2.1. Matched Pair Lie Algebras
2.2. Lie Algebra Homomorphisms
2.3. Euler–Poincaré Equations
3. Symmetric Tensor Spaces
3.1. Symmetric Contravariant Tensors
3.2. Symmetric Covariant Tensors
4. Diffeomorphim Groups and Hamiltonian Vector Fields
4.1. Diffeomorphims and Vector Fields
4.2. Canonical Diffeomorphisms
4.3. Generalized Complete Cotangent Lift
5. Euler–Poincaré Flows
5.1. EP Dynamics on the Space Contravariant Tensor Fields
5.2. Decomposition of EP Dynamics on the Space Contravariant Tensor Fields
5.3. Decomposition of EP Dynamics on Hamiltonian Vector Fields
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Esen, O.; De Lucas, J.; Muñoz, C.S.; Zając, M. Decomposing Euler–Poincaré Flow on the Space of Hamiltonian Vector Fields. Symmetry 2023, 15, 23. https://doi.org/10.3390/sym15010023
Esen O, De Lucas J, Muñoz CS, Zając M. Decomposing Euler–Poincaré Flow on the Space of Hamiltonian Vector Fields. Symmetry. 2023; 15(1):23. https://doi.org/10.3390/sym15010023
Chicago/Turabian StyleEsen, Oğul, Javier De Lucas, Cristina Sardon Muñoz, and Marcin Zając. 2023. "Decomposing Euler–Poincaré Flow on the Space of Hamiltonian Vector Fields" Symmetry 15, no. 1: 23. https://doi.org/10.3390/sym15010023
APA StyleEsen, O., De Lucas, J., Muñoz, C. S., & Zając, M. (2023). Decomposing Euler–Poincaré Flow on the Space of Hamiltonian Vector Fields. Symmetry, 15(1), 23. https://doi.org/10.3390/sym15010023