Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published 1997 | Updated
Book Section - Chapter Open

Mechanical Systems with Symmetry, Variational Principles, and Integration Algorithms

Abstract

This paper studies variational principles for mechanical systems with symmetry and their applications to integration algorithms. We recall some general features of how to reduce variational principles in the presence of a symmetry group along with general features of integration algorithms for mechanical systems. Then we describe some integration algorithms based directly on variational principles using a discretization technique of Veselov. The general idea for these variational integrators is to directly discretize Hamilton's principle rather than the equations of motion in a way that preserves the original systems invariants, notably the symplectic form and, via a discrete version of Noether's theorem, the momentum map. The resulting mechanical integrators are second-order accurate, implicit, symplectic-momentum algorithms. We apply these integrators to the rigid body and the double spherical pendulum to show that the techniques are competitive with existing integrators.

Additional Information

© Springer Science+Business Media New York 1997. Research partially supported by DOE contract DE-FG03-95ER-25251 and the California Institute of Technology. Research partially supported by DOE contract DE-FG03-95ER-25251. / We thank Francisco Armero, Oscar Gonzalez, Abhi Jain, Ben Leimkuhler, Andrew Lewis, Robert MacKay, Richard Murray, George Patrick and Shmuel Weissman for useful discussions or comments.

Attached Files

Updated - MaWe1997.pdf

Files

MaWe1997.pdf
Files (336.1 kB)
Name Size Download all
md5:85113767379169ed389e509b6eb5cb1a
336.1 kB Preview Download

Additional details

Created:
August 19, 2023
Modified:
October 20, 2023