52 citations · 117 across the 5 of their papers we have counts for
5 papers
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…
Nonholonomic Hamilton-Jacobi Theory via Chaplygin Hamiltonization
Tomoki Ohsawa, Oscar E. Fernandez, Anthony M. Bloch +1
We develop Hamilton-Jacobi theory for Chaplygin systems, a certain class of nonholonomic mechanical systems with symmetries, using a technique called Hamiltonization, which transfo…
Controlled Lagrangians and Stabilization of Discrete Mechanical Systems I
Anthony M. Bloch, Melvin Leok, Jerrold E. Marsden +1
Controlled Lagrangian and matching techniques are developed for the stabilization of relative equilibria and equilibria of discrete mechanical systems with symmetry as well as brok…
Controlled Lagrangians and Potential Shaping for Stabilization of Discrete Mechanical Systems
Anthony M. Bloch, Melvin Leok, Jerrold E. Marsden +1
The method of controlled Lagrangians for discrete mechanical systems is extended to include potential shaping in order to achieve complete state-space asymptotic stabilization. New…
Discrete Nonholonomic LL Systems on Lie Groups
Yuri N. Fedorov, Dmitry V. Zenkov
This paper applies the recently developed theory of discrete nonholonomic mechanics to the study of discrete nonholonomic left-invariant dynamics on Lie groups. The theory is illus…