Geometric Linearization for Constraint Hamiltonian Systems

Fuente: arXiv
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Autor principal: Paliathanasis, Andronikos
Formato: Preprint
Publicado: 2024
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author Paliathanasis, Andronikos
author_facet Paliathanasis, Andronikos
contents This study investigates the geometric linearization of constraint Hamiltonian systems using the Jacobi metric and the Eisenhart lift. We establish a connection between linearization and maximally symmetric spacetimes, focusing on the Noether symmetries admitted by the constraint Hamiltonian systems. Specifically, for systems derived from the singular Lagrangian $$ L\left( N,q^{k},\dot{q}^{k}\right) =\frac{1}{2N}g_{ij}\dot{q}^{i}\dot{q}^{j}-NV(q^{k}), $$ where $N$ and $q^{i}$ are dependent variables and $\dim g_{ij}=n$, the existence of $\frac{n\left( n+1\right) }{2}$ Noether symmetries is shown to be equivalent to the linearization of the equations of motion. The application of these results is demonstrated through various examples of special interest. This approach opens new directions in the study of differential equation linearization.
format Preprint
id arxiv_https___arxiv_org_abs_2408_01020
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Geometric Linearization for Constraint Hamiltonian Systems
Paliathanasis, Andronikos
Mathematical Physics
General Relativity and Quantum Cosmology
This study investigates the geometric linearization of constraint Hamiltonian systems using the Jacobi metric and the Eisenhart lift. We establish a connection between linearization and maximally symmetric spacetimes, focusing on the Noether symmetries admitted by the constraint Hamiltonian systems. Specifically, for systems derived from the singular Lagrangian $$ L\left( N,q^{k},\dot{q}^{k}\right) =\frac{1}{2N}g_{ij}\dot{q}^{i}\dot{q}^{j}-NV(q^{k}), $$ where $N$ and $q^{i}$ are dependent variables and $\dim g_{ij}=n$, the existence of $\frac{n\left( n+1\right) }{2}$ Noether symmetries is shown to be equivalent to the linearization of the equations of motion. The application of these results is demonstrated through various examples of special interest. This approach opens new directions in the study of differential equation linearization.
title Geometric Linearization for Constraint Hamiltonian Systems
topic Mathematical Physics
General Relativity and Quantum Cosmology
url https://arxiv.org/abs/2408.01020