Lagrangian mechanics and variational integrators on two-spheres
dc.contributor.author | Lee, Taeyoung | en_US |
dc.contributor.author | Leok, Melvin | en_US |
dc.contributor.author | McClamroch, N. Harris | en_US |
dc.date.accessioned | 2009-09-02T14:38:55Z | |
dc.date.available | 2010-10-05T18:27:29Z | en_US |
dc.date.issued | 2009-08-27 | en_US |
dc.identifier.citation | Lee, Taeyoung; Leok, Melvin; McClamroch, N. Harris (2009). "Lagrangian mechanics and variational integrators on two-spheres." International Journal for Numerical Methods in Engineering 79(9): 1147-1174. <http://hdl.handle.net/2027.42/63605> | en_US |
dc.identifier.issn | 0029-5981 | en_US |
dc.identifier.issn | 1097-0207 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/63605 | |
dc.description.abstract | Euler–Lagrange equations and variational integrators are developed for Lagrangian mechanical systems evolving on a product of two-spheres. The geometric structure of a product of two-spheres is carefully considered in order to obtain global equations of motion. Both continuous equations of motion and variational integrators completely avoid the singularities and complexities introduced by local parameterizations or explicit constraints. We derive global expressions for the Euler–Lagrange equations on two-spheres, which are more compact than existing equations written in terms of angles. Since the variational integrators are derived from Hamilton's principle, they preserve the geometric features of the dynamics such as symplecticity, momentum maps, or total energy, as well as the structure of the configuration manifold. Computational properties of the variational integrators are illustrated for several mechanical systems. In addition, Lie group variational integrators can be used to integrate Lagrangian flows on more general homogeneous spaces. This is achieved by lifting the discrete Hamilton's principle on homogeneous spaces to a discrete variational principle on the Lie group that is constrained by a discrete connection. Copyright © 2009 John Wiley & Sons, Ltd. | en_US |
dc.format.extent | 825996 bytes | |
dc.format.extent | 3118 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.publisher | John Wiley & Sons, Ltd. | en_US |
dc.subject.other | Engineering | en_US |
dc.subject.other | Numerical Methods and Modeling | en_US |
dc.title | Lagrangian mechanics and variational integrators on two-spheres | en_US |
dc.type | Article | en_US |
dc.rights.robots | IndexNoFollow | en_US |
dc.subject.hlbsecondlevel | Engineering (General) | en_US |
dc.subject.hlbsecondlevel | Mechanical Engineering | en_US |
dc.subject.hlbtoplevel | Engineering | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109, U.S.A. | en_US |
dc.contributor.affiliationother | Department of Mechanical and Aerospace Engineering, Florida Institute of Technology, Melbourne, FL 320901, U.S.A. ; Department of Mechanical and Aerospace Engineering, Florida Institute of Technology, Melbourne, FL 320901, U.S.A. | en_US |
dc.contributor.affiliationother | Department of Mathematics, Purdue University, West Lafayette, IN 47907, U.S.A. | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/63605/1/2603_ftp.pdf | |
dc.identifier.doi | 10.1002/nme.2603 | en_US |
dc.identifier.source | International Journal for Numerical Methods in Engineering | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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