Approach of a Particle Statics Problem by Using the Bond-Graph Modeling Method

The paper presents a new approach to the numerical solution of a particle in equilibrium lying on a circle and subjected to the action of a linear spring. The difficulties of solving such a problem and the Mathcad and Simulink based solutions are presented in [1, 2, 3]. The most important difficulties consist in symbolically solving a forth degree trigonometric equation or in solving a complicated trigonometric inequality. This is why a numerical solution is preferred. The use of the bond graph modelling method for solving this problem of equilibrium is presented in this paper. The bond-graph modelling method is designed only for dynamics and the paper presents the possibility of its adaptation for solving this problem of statics of a particle. This approach can be then applied to solve other problems of statics. From the bond graph model the equilibrium equation and the block diagram model can be obtained. The block diagram model is usually preferred in engineering and, for this reason, the block diagram model obtained from the bond-graph model is shown in the paper together with the numerical results obtained after performing the simulations. The results are compared with those previously obtained in [2, 3].