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We establish exactly solvable models for the motion of neutral particles,electrically charged point and spin particles (U(1) symmetry), isospinparticles (SU(2) symmetry), and particles with color charges (SU(3) symmetry)in a gravitational wave background. Special attention is devoted to parametriceffects induced by the gravitational field. In particular, we discussparametric instabilities of the particle motion and parametric oscillations ofthe vectors of spin, isospin, and color charge.Comment: 26 pages, to be published in J. Math. Phy

Parametric phenomena of the particle dynamics in a periodic gravitational wave field