University of Surrey

Test tubes in the lab Research in the ATI Dance Research

Stability of Poisson equilibria and Hamiltonian relative equilibria by energy methods

Patrick, GW, Roberts, M and Wulff, Claudia (2004) Stability of Poisson equilibria and Hamiltonian relative equilibria by energy methods ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 174 (3). pp. 301-344.

[img]
Preview
Text
stabRE.pdf
Available under License : See the attached licence file.

Download (463kB) | Preview
[img]
Preview
Text (licence)
SRI_deposit_agreement.pdf
Available under License : See the attached licence file.

Download (33kB) | Preview
[img] Text (deleted)
0201239v1.pdf
Restricted to Repository staff only
Available under License : See the attached licence file.

Download (450kB)

Abstract

We develop a general stability theory for equilibrium points of Poisson dynamical systems and relative equilibria of Hamiltonian systems with symmetries, including several generalisations of the Energy-Casimir and Energy-Momentum Methods. Using a topological generalisation of Lyapunov’s result that an extremal critical point of a conserved quantity is stable, we show that a Poisson equilibrium is stable if it is an isolated point in the intersection of a level set of a conserved function with a subset of the phase space that is related to the topology of the symplectic leaf space at that point. This criterion is applied to generalise the energy-momentum method to Hamiltonian systems which are invariant under non-compact symmetry groups for which the coadjoint orbit space is not Hausdorff. We also show that a G-stable relative equilibrium satisfies the stronger condition of being A-stable, where A is a specific group-theoretically defined subset of G which contains the momentum isotropy subgroup of the relative equilibrium. The results are illustrated by an application to the stability of a rigid body in an ideal irrotational fluid.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
NameEmailORCID
Patrick, GWUNSPECIFIEDUNSPECIFIED
Roberts, MUNSPECIFIEDUNSPECIFIED
Wulff, ClaudiaC.Wulff@surrey.ac.ukUNSPECIFIED
Date : 1 December 2004
Identification Number : 10.1007/s00205-004-0322-9
Copyright Disclaimer : The final publication is available at Springer via http://dx.doi.org/10.1007/s00205-004-0322-9
Uncontrolled Keywords : Science & Technology, Physical Sciences, Technology, Mathematics, Interdisciplinary Applications, Mechanics, Mathematics, MATHEMATICS, INTERDISCIPLINARY APPLICATIONS, MECHANICS, POINT VORTICES, NONLINEAR STABILITY, UNDERWATER VEHICLE, COINCIDENT CENTERS, MOMENTUM METHOD, SYMMETRY, SYSTEMS, PERSISTENCE, DYNAMICS, SPHERE
Related URLs :
Depositing User : Symplectic Elements
Date Deposited : 20 Jan 2015 19:08
Last Modified : 16 Aug 2017 09:43
URI: http://epubs.surrey.ac.uk/id/eprint/805293

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year


Information about this web site

© The University of Surrey, Guildford, Surrey, GU2 7XH, United Kingdom.
+44 (0)1483 300800