Fundamental constraints on uncertainty evolution in Hamiltonian Systems

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Title:	Fundamental constraints on uncertainty evolution in Hamiltonian Systems
Authors:	Hsiao, Fu-yuen;Scheeres, D.J.
Contributors:	淡江大學航空太空工程學系
Date:	2006-06
Issue Date:	2010-01-11 15:12:19 (UTC+8)
Abstract:	A realization of Gromov's nonsqueezing theorem and its applications to uncertainty analysis in Hamiltonian systems are studied in this paper. Gromov's nonsqueezing theorem describes a fundamental property of symplectic manifolds, however, this theorem is usually started in terms of topology and its physical meaning is vague. In this paper we introduce a physical interpretation of the linear symplectic width, which is the lower bound in the nonsqueezing theorem, given the eigenstructure of a positive-definite, symmetric matrix. Since a positive-definite, symmetric matrix always represents the uncertainty ellipsoid in practical mechanics problems, our study can be applied to uncertainty analysis. We find a fundamental inequality for the evolving uncertainty in a linear dynamical system and provide some numerical examples.
Relation:	Proceedings of the American Control Conference, 2006, 6p.
DOI:	10.1109/ACC.2006.1657520
Appears in Collections:	[Graduate Institute & Department of Aerospace Engineering] Proceeding

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