Average-preserving symmetries and equipartition in linear Hamiltonian systems
DSpace at IIT Bombay
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Title |
Average-preserving symmetries and equipartition in linear Hamiltonian systems
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Creator |
BHAT, SP
BERNSTEIN, DENNIS S |
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Subject |
matrix algebra
natural frequencies theorem proving set theory |
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Description |
This paper analyzes equipartition in linear Hamiltonian systems in a deterministic setting. We consider the group of phase space symmetries of a stable linear Hamiltonian system, and characterize the subgroup of symmetries whose elements preserve the time averages of quadratic functions along the trajectories of the system. As a corollary, we show that if the system has simple eigenvalues, then every symmetry preserves averages of quadratic functions. As an application of our results to linear undamped lumped-parameter systems, we provide a novel proof of the virial theorem using symmetry. We also show that under the assumption of distinct natural frequencies, the time-averaged energies of two identical substructures of a linear undamped structure are equal. Examples are provided to illustrate the results.
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Publisher |
IEEE
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Date |
2009-04-03T09:06:17Z
2011-11-28T07:43:05Z 2011-12-15T09:57:09Z 2009-04-03T09:06:17Z 2011-11-28T07:43:05Z 2011-12-15T09:57:09Z 2004 |
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Type |
Article
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Identifier |
Proceedings of the 43rd IEEE Conference on Decision and Control (V 2), Nassau, The Bahamas, 17 December 2004, 2155-2160
0-7803-8682-5 10.1109/CDC.2004.1430367 http://hdl.handle.net/10054/1133 http://dspace.library.iitb.ac.in/xmlui/handle/10054/1133 |
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Language |
en
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