Extremum property of constraint reactions

The problem of finding constraint reactions in mechanical systems is discussed. It is shown that in a number of cases its solution reduces to finding the minimum of the generalized potential energy, whose expression depends on the active forces and the inertial forces and includes the strain energy. The condition of a minimum value provides a means, in particular, to single out “the most realistic” solution of statically indeterminate problems. In systems with Coulomb static friction, verification of the equilibrium conditions can be reduced to a convex minimization problem. Typical expressions for the generalized potential energy in systems with kinetic friction with one bilateral or unilateral constraint, which enable the dynamics of the system to be determined in cases of indeterminancy, are presented.