The Euler-Poincaré equations and double bracket dissipation
dc.contributor.author | Ratiu, Tudor S. | en_US |
dc.contributor.author | Krishnaprasad, P. S. | en_US |
dc.contributor.author | Bloch, Anthony M. | en_US |
dc.contributor.author | Marsden, Jerrold E. | en_US |
dc.date.accessioned | 2006-09-11T17:50:45Z | |
dc.date.available | 2006-09-11T17:50:45Z | |
dc.date.issued | 1996-01 | en_US |
dc.identifier.citation | Bloch, Anthony; Krishnaprasad, P. S.; Marsden, Jerrold E.; Ratiu, Tudor S.; (1996). "The Euler-Poincaré equations and double bracket dissipation." Communications in Mathematical Physics 175(1): 1-42. <http://hdl.handle.net/2027.42/46491> | en_US |
dc.identifier.issn | 1432-0916 | en_US |
dc.identifier.issn | 0010-3616 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/46491 | |
dc.description.abstract | This paper studies the perturbation of a Lie-Poisson (or, equivalently an Euler-Poincaré) system by a special dissipation term that has Brockett's double bracket form. We show that a formally unstable equilibrium of the unperturbed system becomes a spectrally and hence nonlinearly unstable equilibrium after the perturbation is added. We also investigate the geometry of this dissipation mechanism and its relation to Rayleigh dissipation functions. This work complements our earlier work (Bloch, Krishnaprasad, Marsden and Ratiu [1991, 1994]) in which we studied the corresponding problem for systems with symmetry with the dissipation added to the internal variables; here it is added directly to the group or Lie algebra variables. The mechanisms discussed here include a number of interesting examples of physical interest such as the Landau-Lifschitz equations for ferromagnetism, certain models for dissipative rigid body dynamics and geophysical fluids, and certain relative equilibria in plasma physics and stellar dynamics. | en_US |
dc.format.extent | 2314669 bytes | |
dc.format.extent | 3115 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Springer-Verlag | en_US |
dc.subject.other | Statistical Physics | en_US |
dc.subject.other | Quantum Physics | en_US |
dc.subject.other | Nonlinear Dynamics, Complex Systems, Chaos, Neural Networks | en_US |
dc.subject.other | Quantum Computing, Information and Physics | en_US |
dc.subject.other | Physics | en_US |
dc.subject.other | Relativity and Cosmology | en_US |
dc.subject.other | Mathematical and Computational Physics | en_US |
dc.title | The Euler-Poincaré equations and double bracket dissipation | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Physics | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Mathematics, University of Michigan, 48109, Ann Arbor, MI, USA | en_US |
dc.contributor.affiliationother | Department of Electrical Engineering and Institute for Systems Research, University of Maryland, 20742, College Park, MD, USA | en_US |
dc.contributor.affiliationother | Control and Dynamical Systems 104-44, California Institute of Technology, 91125, Pasadena, CA, USA | en_US |
dc.contributor.affiliationother | Department of Mathematics, University of California, 95064, Santa Cruz, CA, USA | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/46491/1/220_2005_Article_BF02101622.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1007/BF02101622 | en_US |
dc.identifier.source | Communications in Mathematical Physics | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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