Open AccessEuler-Poincaré reduction for systems with configuration space isotropy
Author(s) -
Jeffrey K. Lawson,
Tanya Schmah,
Cristina Stoica
Publication year - 2011
Publication title -
the journal of geometric mechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.511
H-Index - 17
eISSN - 1941-4897
pISSN - 1941-4889
DOI - 10.3934/jgm.2011.3.261
Subject(s) - isotropy , homogeneous space , euler's formula , euler equations , reduction (mathematics) , space (punctuation) , phase space , mathematics , mathematical analysis , lagrangian , variational principle , equations of motion , motion (physics) , configuration space , state space , euler angles , classical mechanics , physics , geometry , computer science , quantum mechanics , statistics , operating system
This paper concerns Lagrangian systems with symmetries, near points with configuration space isotropy. Using twisted parametrisations corresponding to phase space slices based at zero points of tangent fibres, we deduce reduced equations of motion, which are a hybrid of the Euler-Poincare and Euler-Lagrange equations. Further, we state a corresponding variational principle.
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