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Please use this identifier to cite or link to this item: http://dspace.library.iitb.ac.in/jspui/handle/10054/12223

Title: Average-preserving symmetries and energy equipartition in linear Hamiltonian systems
Authors: BHAT, SP
BERNSTEIN, DS
Keywords: dissipative dynamical-systems
Issue Date: 2009
Publisher: SPRINGER LONDON LTD
Citation: MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 21(2), 127-146
Abstract: 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.
URI: 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
ISSN: 0932-4194
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