A method for setting equations of motion for a system of solids with nonholonomic constraints is proposed. The construction of dynamical equations involves the application of a matrix form of recording. Based on the analysis of systems with one, two, or three links, generalizations are derived for the matrices contained in the matrix method for constructing a system with an arbitrary finite number of links. An algorithm for describing the model of a snowboarder with an arbitrary finite number of links of a complex structure with variable length, sliding on an absolutely solid ski, is compiled. A non-holonomic constraint occurs in the ski-snow contact zone. The problem of constructing a stable motion of a system with variable-length links using the link stabilization method is considered. The control is implemented by changing the length of the links and changing the angles between the links. The connection of the links is modeled by two cylindrical joints, which provide significant mechanical strength, simplicity of design and location of the control drives.
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