发表机构
Instituto de Matemática e Estatística, Universidade Federal da Bahia; Faculdade de Ciências Exatas e Naturais - Departamento de Matemática e Estatística, Universidade do Estado do Rio Grande do Norte（巴伊亚联邦大学数学与统计学院; 北里奥格兰德州州立大学理学院数学与统计系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究构建了锥形伪芬斯勒流形上保守力学系统的几何框架，推广了经典黎曼力学，建立了守恒律、完备性准则及约束力存在唯一性，为各向异性动力学提供统一几何基础。
AI 中文摘要
我们为以锥形伪芬斯勒流形为模型的保守力学系统构建了几何框架，将经典黎曼与半黎曼力学扩展至各向异性几何领域。在此框架下，我们定义了雅可比型伪芬斯勒度量，并证明固定能量的运动经重新参数化后对应该度量的测地线；通过推广的诺特定理，在合适的对称性假设下建立了能量与动量守恒关系，同时给出雅可比度量及力学系统完备性的新分析准则。此外，对于带有完整与非完整约束的力学系统，我们证明了满足达朗贝尔原理的约束力的存在性与唯一性。这些结果为受约束及无约束的各向异性动力学提供了统一的几何基础。
英文摘要
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.
Comments19 pages
