2025/11/02 by Zonghai Li, Li, Zonghai · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Spacecraft Dynamics and Control
paper · pdf · doi:10.48550/arxiv.2511.01004
openalex publication_date 2025/11/02 · openalex created_date 2025/11/06 · openalex updated_date 2026/07/28
This paper develops a systematic approach to the geometrization of dynamics from the viewpoint of the geodesic equation. The method promotes a semispray to a spray through the imposition of suitable dynamical constraints, and the associated metric structure is extracted via reparameterization. When applied to static spacetimes, this spray-to-metric framework recovers the optical metric, the Jacobi metric for massive particles, and its generalization for charged particles in electromagnetic fields. We further show that a Randers-type Finsler metric arises naturally in the planar circular restricted three-body problem. By establishing a direct pathway from equations of motion to metric structures, this work offers a geometric perspective, independent of the traditional variational framework, may provide a basis for further studies on dynamical systems.