106 citations · 677 across the 72 of their papers we have counts for
6 papers · 1 filter
Hamel's Formalism and Variational Integrators on a Sphere
Dmitry V. Zenkov, Melvin Leok, Anthony M. Bloch
This paper discusses Hamel's formalism and its applications to structure-preserving integration of mechanical systems. It utilizes redundant coordinates in order to eliminate multi…
Dynamics and Control of a Chain Pendulum on a Cart
Taeyoung Lee, Melvin Leok, N. Harris McClamroch
A geometric form of Euler-Lagrange equations is developed for a chain pendulum, a serial connection of rigid links connected by spherical joints, that is attached to a rigid ca…
Dirac Structures and Hamilton-Jacobi Theory for Lagrangian Mechanics on Lie Algebroids
Melvin Leok, Diana Sosa
This paper develops the notion of implicit Lagrangian systems on Lie algebroids and a Hamilton--Jacobi theory for this type of system. The Lie algebroid framework provides a natura…
Spectral Variational Integrators
James Hall, Melvin Leok
In this paper, we present a new variational integrator for problems in Lagrangian mechanics. Using techniques from Galerkin variational integrators, we construct a scheme for numer…
A novel formulation of point vortex dynamics on the sphere: geometrical and numerical aspects
Joris Vankerschaver, Melvin Leok
In this paper, we present a novel Lagrangian formulation of the equations of motion for point vortices on the unit 2-sphere. We show first that no linear Lagrangian formulation exi…
The Hamilton-Pontryagin Principle and Multi-Dirac Structures for Classical Field Theories
Joris Vankerschaver, Hiroaki Yoshimura, Melvin Leok
We introduce a variational principle for field theories, referred to as the Hamilton-Pontryagin principle, and we show that the resulting field equations are the Euler-Lagrange equ…