The extremal property of the constraint reactions of systems of connected bodies

Abstract

The extremal property of the forces and moments of reactions in the joints of mechanical systems consisting of a carrier and bodies connected to it is investigated, based on the principle of least constraint. The problem of minimizing the functional of the linear and angular accelerations of bodies, taking into account holonomic retaining constraints in which there is active friction is solved by the method of undetermined multipliers. It is shown that their values for the actual motion of the bodies coincide with the forces and moments of the constraint reactions, and the least constraint is determined. The results obtained are interpreted from the positions of elasticity theory. The separation of the stages of rockets is considered on the basis of the principle of least constraint.