Singularities in the Expression of the Kinetic Energy of a System of Particles Subject to Holonomous Constraints

In the textbooks on classical mechanics normally adopted for courses on mechanical engineering, there is no mention of the paradoxical fact that a material system subject to holonomous constraints can exhibit singular configurations for which the cross-products of their generalized velocities, not all identically nil, give rise to a zero value for the kinetic energy. Given the importance of this subject for the analysis of dynamic systems, and as a contribution to education in mechanics, we analyse in this article a material system composed of discrete masses subject to holonomous constraints and exhibiting the mentioned behaviour. After deriving an analytical expression for the kinetic energy of the system, numerical simulations permit the identification of some singular material configurations for which the initial statement holds.