This paper is devoted to the computation of the dynamical and geometrical phases of a classical cyclic evolution for a time-periodic linear Euler equation on a Lie algebra. Sufficient conditions for the representation of the geometrical phase in terms of the symplectic form of a coadjoint orbit are given. For a 1-parameter family of linear periodic Euler equations, the parameter evolution of the phase angles is described. These results are illustrated in the case of 3-dimensional Lie algebras. Copyright © 2005 by MAIK "Nauka/Interperiodica" (Russia).
|Original language||American English|
|Number of pages||24|
|Journal||Russian Journal of Mathematical Physics|
|State||Published - 1 Jul 2005|