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Using the standard canonical formalism, the equations of mechanics andkinetics in the Friedmann-Lemaitre-Robertson-Walker (FLRW) space-times inCartesian coordinates have been obtained. The transformation law of thegeneralized momentum under the shift of the origin of the coordinate system hasbeen found, and the form invariance of the Hamiltonian function relative to theshift transformation has been proved. The general solution of the collisionlessBoltzmann equation has been found. In the case of the homogeneous distributionthe solutions of the kinetic equation for several simple, but important forapplications, cases have been obtained.

Mechanics and kinetics in the Friedmann-Lemaitre-Robertson-Walker space-times