1999/05/31 by L. Mangiarotti, Mangiarotti, L., G. Sardanashvily +1
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Dynamics and Control of Mechanical Systems #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geological Modeling and Analysis #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/9905107
17 pages, LaTeX
arxiv created 1999/05/31 · openalex publication_date 1999/05/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that any second order dynamic equation on a configuration space X→ R of nonrelativistic mechanics can be seen as a geodesic equation with respect to some (nonlinear) connection on the tangent bundle TX→ X of relativistic velocities. We compare relativistic and nonrelativistic geodesic equations, and study the Jacobi vector fields along nonrelativistic geodesics.