In many complex mechanical systems the transmissions with nonholonomic characteristics as transmitters with changeable transmission ratio are found. This type of transmission has the connections of differential character between transmissions elements. Nonholonomic mechanical system can be recognized as variable-speed drives, contained in many complex systems of modern techniques. The aim of this paper is to give one of approach to dynamically description the behavior one of the general examples of transmissions with nonholonomic characteristics and to estimate the stability of working system with changeable working regime. For dynamically description of the mechanical nonholonomic system Appell`s differential equations are used. By numerical solving of differential equations of moving we get the answer concerning the working stability as well as the dynamical and kinematics behavior of observed system. The obtained results will serve as one of the constraint in choosing optimal parameters in the synthesis of power transmissions.
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