The realization of unilateral constraints in mechanical systems with kinetic energy decay

A method of realizing unilateral constraints by introducing a small parameter into the kinetic energy, such that the kinetic energy of the system degenerates on a certain manifold in configuration space when the parameter is equal to zero, is considered. The behaviour of the system in the neighbourhood of the degeneracy manifold in the multidimensional case when the small parameter approaches zero is investigated. The results obtained are used in the problem of the motion of a double mathematical pendulum when the mass of the point closest to the suspension point is small.