Phase space geometry for constrained Lagrangian systems

TL;DR

This paper explores the geometric structure of phase space in constrained Lagrangian systems, unifying Lagrangian and Hamiltonian formalisms through invariant geometric objects and foliation theory.

Contribution

It provides an invariant geometric framework that unifies the Lagrangian and Hamiltonian descriptions of constrained dynamical systems.

Findings

Unified geometric description of constrained phase space

Invariant formulation using foliation structures

Insights into the geometry of degenerate Lagrangian systems

Abstract

We study geometry of the phase space for finite-dimensional dynamical systems with degenerate Lagrangians. The Lagrangian and Hamiltonian constraint formalisms are treated as different local-coordinate pictures of the same invariant procedure. The invariant description is given in terms of geometrical objects associated with the structure of foliation on the phase space.