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|Title:||Average-preserving symmetries and equipartition in linear Hamiltonian systems|
BERNSTEIN, DENNIS S
|Citation:||Proceedings of the 43rd IEEE Conference on Decision and Control (V 2), Nassau, The Bahamas, 17 December 2004, 2155-2160|
|Abstract:||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.|
|Appears in Collections:||Proceedings papers|
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