Bifurcation of self-excited rigid bodies subjected to small perturbation torques

The attitude motion of self-excited rigid bodies subjected to small perturbation torques is investigated by using the version of the Melnikov method developed for slowly varying oscillators. For this purpose the Deprit variables are introduced to transform the equations of motion into a form describing a slowly varying oscillator. For self-excited rigid bodies subjected to small periodic torques, the existence of transversal intersections of heteroclinic orbits has been found for certain parameter ranges. For self-excited rigid bodies subjected to small constant torques, the relationship between the bifurcation (nontransverse) of heteroclinic orbits and the system parameters is given.