Analog Raychaudhuri Equation in Mechanics

Usually, in mechanics, we obtain the trajectory of a particle given force field by solving Newton’s second law with chosen initial conditions. In contrast, through our work here, first demonstrate how one may analyze behaviour suitably defined family trajectories mechanical system. Such an approach leads us to develop mechanics analogue following well-known Raychaudhuri equation largely studied Riemannian geometry and general relativity. The idea geodesic focusing, which is more familiar relativist, appears be analogous meeting system within finite time. Applying results case simple pendula, relevant quantitative consequences. Thereafter, set up perform straightforward experiment based on two pendula. experimental this are found tally well proposed theoretical model. summary, theory related provide way understand essence fairly involved concept advanced physics from elementary standpoint.