Dynamical Systems on Bundles

TL;DR

This paper explores the geometric formulation of Hamiltonian and Lagrangian dynamical systems on tangent and cotangent bundles, providing insights into their mathematical structure and physical implications.

Contribution

It develops a geometric framework for Hamiltonian and Lagrangian systems on bundles, integrating horizontal and vertical distributions for a unified approach.

Findings

Geometrical structures of Hamiltonian systems are characterized on bundles.

Lagrangian systems are formulated using bundle geometry.

Physical interpretations of the geometric results are discussed.

Abstract

In this study, Hamiltonian and Lagrangian theories, which are mathematical models of mechanical systems, are structured on the horizontal and the vertical distributions of tangent and cotangent bundles. In the end, the geometrical and physical results related to Hamiltonian and Lagrangian dynamical systems are concluded.