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math.SG1999
The Landau-Lifshitz Equation by Semidirect Product Reduction
G. W. Patrick
The Landau-Lifshitz equation is derived as the reduction of a geodesic flow on the group of maps into the rotation group. Passing the symmetries of spatial isotropy to the reduced…
math.SG1999
Dynamics near Relative Equilibria: Nongeneric Momenta at a 1:1 Group-Reduced Resonance
G. W. Patrick
An interesting situation occurs when the linearized dynamics of the shape of a formally stable Hamiltonian relative equilibrium at nongeneric momentum 1:1 resonates with a frequenc…