Extension of the Bernoulli's case of brachistochronic motion to the multibody system having the form of a kinematic chain with external constraints

摘要

The system of rigid bodies forming a kinematic chain subject to the external constraints is considered. The conditions imposed on the form of external constraints, under which the system considered moves in a homogeneous field of gravity from the given initial position to the given final positon so that time of the motion takes its minimal value, are found. A complete analogy of such a motion of the system with the familiar Bernoulli's case of a brachistochronic motion of a Particle in a homogeneous field of gravity is established. Results of the paper are illustrated by an example.