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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
 
Creator BHAT, SP
BERNSTEIN, DENNIS S
 
Subject matrix algebra
natural frequencies
theorem proving
set theory
 
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.
 
Publisher IEEE
 
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
 
Type Article
 
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
 
Language en