# Line Integral Solution of Hamiltonian Systems with Holonomic Constraints

## TL;DR

This paper introduces a second-order energy-conserving numerical method for Hamiltonian systems with holonomic constraints, utilizing a line integral framework to ensure accuracy and conservation properties.

## Contribution

The paper presents a novel line integral-based approach for energy-conserving approximations in constrained Hamiltonian systems, advancing numerical methods in this area.

## Key findings

- The method conserves energy accurately in numerical experiments.
- Numerical results validate the theoretical properties of the proposed approach.
- The approach is applicable to a range of holonomic constrained systems.

## Abstract

In this paper, we propose a second-order energy-conserving approximation procedure for Hamiltonian systems with holonomic constraints. The derivation of the procedure relies on the use of the so-called line integral framework. We provide numerical experiments to illustrate theoretical findings.