On the Geodesic Form of Non-Relativistic Dynamic Equations

Abstract

It is shown that any second order dynamic equation on a configuration bundle $Q\to R$ of non-relativistic mechanics is equivalent to a geodesic equation with respect to a (non-linear) connection on the tangent bundle $TQ\to Q$. The case of quadratic dynamic equations is analyzed in details. The equation for Jacobi vector fields is constructed and investigated by the geometric methods.

15 pages, LaTeX

References in corpus (2)

• Non-standard connections in classical mechanics
• Nonholonomic Constraints in Time-Dependent Mechanics

Cited by in corpus (3)

• Quantum mechanics with time-dependent parameters
• Relative non-relativistic mechanics
• Geometric quantization of non-relativistic and relativistic Hamiltonian mechanics