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Average-preserving symmetries and energy equipartition in linear Hamiltonian systems

DSpace at IIT Bombay

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Title Average-preserving symmetries and energy equipartition in linear Hamiltonian systems
 
Creator BHAT, SP
BERNSTEIN, DS
 
Subject dissipative dynamical-systems
equipartition
hamiltonian systems
symmetry
average-preserving symmetry
virial theorem
center subgroups
 
Description This paper analyzes energy 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, which states that the total energy is equipartitioned on the average between the kinetic energy and the potential energy. 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 SPRINGER LONDON LTD
 
Date 2011-08-30T06:44:47Z
2011-12-26T12:58:48Z
2011-12-27T05:49:22Z
2011-08-30T06:44:47Z
2011-12-26T12:58:48Z
2011-12-27T05:49:22Z
2009
 
Type Article
 
Identifier MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 21(2), 127-146
0932-4194
http://dx.doi.org/10.1007/s00498-009-0039-2
http://dspace.library.iitb.ac.in/xmlui/handle/10054/12223
http://hdl.handle.net/10054/12223
 
Language en