On the brachistochronic motion of mechanical systems with unilateral constraints

The problem of brachistochronic motion of a two-degree of freedom mechanical system is considered. The ideal bilateral constraints and one unilateral constraint with Coulomb friction are imposed on the system. It has been assumed that the components of the metric tensor are constant. After introducing the transformation of generalized coordinates, whereby the quadratic form of kinetic energy is reduced to a canonical form, the considered problem is geometrically interpreted as the motion of a representative point in a two-dimensional Euclidean space. Thus, the analogy with the brachistochronic motion of a particle along a curve which is treated as a unilateral constraint is achieved. The results are illustrated via an example.

► Brachistochronic motion of a two-degree of freedom mechanical system is considered.
► A unilateral constraint with Coulomb friction is imposed.
► The concept of a representative point in a two-dimensional Euclidean space is used.
► The analogy with the brachistochrone problem of a particle is pointed.