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余伴随轨道上的噪声与耗散

Noise and Dissipation on Coadjoint Orbits.

作者信息

Arnaudon Alexis, De Castro Alex L, Holm Darryl D

机构信息

1Department of Mathematics, Imperial College, London, SW7 2AZ UK.

2Departamento de Matemática, PUC-Rio, Rio de Janeiro, 22451-900 Brazil.

出版信息

J Nonlinear Sci. 2018;28(1):91-145. doi: 10.1007/s00332-017-9404-3. Epub 2017 Jul 17.

DOI:10.1007/s00332-017-9404-3
PMID:29367809
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC5756579/
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.

摘要

我们通过将噪声和耗散纳入由对称性约化理论产生的力学系统（包括半直积扩展），推导并研究余伴随轨道上的随机耗散动力学。当李代数是半单的且顶部李雅普诺夫指数为正时，对于这类一般系统找到了随机吸引子。我们详细研究了两个典型例子，即自由刚体和重陀螺，找到了它们的随机可积约化，并展示了其随机吸引子的数值模拟。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a5ee/5756579/851857571cc2/332_2017_9404_Fig8_HTML.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a5ee/5756579/851857571cc2/332_2017_9404_Fig8_HTML.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a5ee/5756579/ead53c2ace33/332_2017_9404_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a5ee/5756579/4fd09eeecc21/332_2017_9404_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a5ee/5756579/be21e85c99df/332_2017_9404_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a5ee/5756579/f5766717c0d3/332_2017_9404_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a5ee/5756579/6a18210cca24/332_2017_9404_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a5ee/5756579/851857571cc2/332_2017_9404_Fig8_HTML.jpg

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本文引用的文献

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