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Omni wheel is defined as one having rollers along its rim. Respectively omni vehicle is one equipped by omni wheels. Several steps of development of dynamical model of the omni vehicle multibody system are implemented. Essential parameters of the model: (a) number of rollers per the wheel, and (b) angle of the roller axis inclination to the wheel plane, are introduced. Initially, dynamics of the free roller moving in a field of gravity and having a unilateral contact constraint with horizontal surface is modeled. The contact tracking using simplified and efficient algorithm turns out being possible. On the next stage the omni wheel model is developed and debugged. After that the whole vehicle model is assembled as a container class having arrays of objects as instantiated classes / models of omni wheels and joints. Dynamical properties of the resulting model are illustrated via numerical experiments.