Conic Pseudo-Finslerian Mechanical Systems
Abstract
We develop a geometric framework for conservative mechanical systems modeled on conic pseudo-Finslerian manifolds, extending classical Riemannian and semi-Riemannian mechanics to anisotropic geometries. In this setting, we define a Jacobi-type pseudo-Finslerian metric and demonstrate that motions of fixed energy correspond, up to reparametrization, to its geodesics. We establish energy and momentum conservation under suitable symmetry assumptions via a generalized Noether's theorem, and provide new analytical criteria for the completeness of both the Jacobi metric and the mechanical system. Furthermore, for mechanical systems with holonomic and non-holonomic constraints, we prove the existence and uniqueness of reaction forces satisfying d'Alembert's principle. These results provide a unified geometric foundation for constrained and unconstrained anisotropic dynamics.
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BibTeX
@misc{alves2026conic,
title = {{Conic Pseudo-Finslerian Mechanical Systems}},
author = {Benigno Oliveira Alves and Glaene S. S. Mendonça},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03909},
eprint = {2609.03909},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03909},
}
RIS
TY - UNPB
TI - Conic Pseudo-Finslerian Mechanical Systems
AU - Benigno Oliveira Alves
AU - Glaene S. S. Mendonça
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03909
UR - https://arxiv.org/abs/2609.03909
AB - We develop a geometric framework for conservative mechanical systems modeled on conic pseudo-Finslerian manifolds, extending classical Riemannian and semi-Riemannian mechanics to anisotropic geometries. In this setting, we define a Jacobi-type pseudo-Finslerian metric and demonstrate that motions of fixed energy correspond, up to reparametrization, to its geodesics. We establish energy and momentum conservation under suitable symmetry assumptions via a generalized Noether's theorem, and provide new analytical criteria for the completeness of both the Jacobi metric and the mechanical system. Furthermore, for mechanical systems with holonomic and non-holonomic constraints, we prove the existence and uniqueness of reaction forces satisfying d'Alembert's principle. These results provide a unified geometric foundation for constrained and unconstrained anisotropic dynamics.
ER -