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A special mathematical apparatus of monomial matrices, is applied to the simulation of programmed transfer and rotation of a high-speed vehicle in space. Programmed transfer is described by a vector-hodograph in the class of spiral-helix trajectories. A method for constructing the hodograph of programmed motion is proposed. The kinetics of the programmed motion of a transport vehicle is considered in the forms of the Newton equations, Euler equations, Euler-Lagrange differential equations and is represented by quaternion matrices. The principle of kinetostatics is applied to the determination the resultant vector of driving forces and the resultant moment of force providing programmed transfer and rotation. A cascade method has been developed for the equivalent distribution of the resultant vector of driving forces and the resultant moment of force over the reference points, establishing the necessary reactivity of the constraint. The obtained analytical results are informative, adapted to computer technologies, intended for use in computational experiments to solve engineering problems of dynamic design of high-speed carriages of transport.