Mathematical Framework and Non-Linear Modeling of the Mechanical System. Part I: Rigid Body Kinematics - Haddout, S.; Rhazi, M.; Faik, S.E.; Soukri, A. (Journal of Vibration Testing and System Dynamics, 2026)
In the present paper, a problem of a free rigid body motion in mechanical system is analyzed from a video capture webcam (Sony Cybershot 10.1 M.P). The problem subjected to kinematic characteristics and relative trajectories are theoretically and analytically solved. Subsequently, the solution is quantitatively verified by a new experiment procedure, constructed by the authors. The geometrical treatments of the absolute experimental trajectories of two points of the body, allow determining the relative trajectory of a point from the other point. The kinematic parameters optimization, i.e., translational velocity, instantaneous velocity of rotation and initial kinematic conditions, are obtained, solving non-linear least-squares problems, based on Levenberg-Marquardt’s algorithm. On the other hand, the response surfaces of the objective function and the sensitivity analysis of the different initial estimates of the analytical model parameters are also discussed. The comparison of the theoretical study results with experimental output shows that there are instruments to directly verify rather abstract mathematical theories even on the general mechanics program. Moreover, combining the theoretical description of the problem with an appropriate laboratory experiment and computational optimization procedures, gives a more exhaustive view of the physical problem as a whole.