Nonholonomic Constraints in Time-Dependent Mechanics

TL;DR

This paper develops a Hamiltonian formalism for time-dependent mechanical systems with ideal nonholonomic constraints, providing a new way to analyze the reaction forces involved.

Contribution

It introduces a Hamiltonian framework for nonholonomic constraints in time-dependent mechanics using the vertical tangent bundle extension.

Findings

Derived the reaction force expression for nonholonomic constraints.

Constructed the Hamiltonian formalism on the vertical tangent bundle.

Extended Hamiltonian methods to time-dependent nonholonomic systems.

Abstract

The constraint reaction force of ideal nonholonomic constraints in time-dependent mechanics on a configuration bundle $Q\to R$ is obtained. Using the vertical extension of Hamiltonian formalism to the vertical tangent bundle $VQ$ of $Q\to R$, the Hamiltonian of a nonholonomic constrained system is constructed.