A revisitation of the paradox of discontinuous trajectory for a mass particle moving on a taut string

A nonlinear extended regularized model of taut string carrying a moving point mass is proposed with the intent to contribute to the solution of the paradox of particle’s discontinuous trajectory. Introducing a coupling between transversal and longitudinal string displacements, an additional equation expressing the so-called wave pressure force arises whose closed-form expression can be obtained imposing that the load-structure combined system is dissipation free. In this context, paradoxical situations in the classic model lead to the emergence of wave resistance forces in the new proposed model that can significantly influence the motion of the inertia particle. Comparisons between classic and improved solutions are presented highlighting the possibility that mass particle can reach the remote support, or can return to the initial support, or do not come to any of the string support according to the values of four dimensionless parameters governing the extended problem.