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Noise and Dissipation on Coadjoint Orbits

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10.1007%2Fs00332-017-9404-3.pdfPublished version4.16 MBAdobe PDFView/Open
Title: Noise and Dissipation on Coadjoint Orbits
Authors: Arnaudon, A
De Castro, AL
Holm, D
Item Type: Journal Article
Abstract: We derive and study stochastic dissipative dynamics on coadjoint orbits by incorporating noise and dissipation into mechanical systems arising from the theory of reduction by symmetry, including a semidirect product extension. Random attractors are found for this general class of systems when the Lie algebra is semi-simple, provided the top Lyapunov exponent is positive. We study in details two canonical examples, the free rigid body and the heavy top, whose stochastic integrable reductions are found and numerical simulations of their random attractors are shown.
Issue Date: 17-Jul-2017
Date of Acceptance: 12-Jun-2017
URI: http://hdl.handle.net/10044/1/33415
DOI: https://dx.doi.org/10.1007/s00332-017-9404-3
ISSN: 0938-8974
Publisher: Springer Verlag
Start Page: 91
End Page: 145
Journal / Book Title: Journal of Nonlinear Science
Volume: 28
Issue: 1
Copyright Statement: © The Author(s) 2017. This article is an open access publication
Keywords: Science & Technology
Physical Sciences
Technology
Mathematics, Applied
Mechanics
Physics, Mathematical
Mathematics
Physics
Stochastic geometric mechanics
Euler-Poincare theory
Coadjoint orbits
Invariant measures
Random attractors
Lyapunov exponents
EULER-POINCARE EQUATIONS
RIGID-BODY
DYNAMICAL-SYSTEMS
POISSON BRACKETS
SELECTIVE DECAY
ATTRACTORS
STABILITY
MECHANICS
FLUIDS
math.DS
math-ph
math.MP
nlin.CD
0102 Applied Mathematics
Fluids & Plasmas
Publication Status: Published
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences