Vibro-impact dynamics of two rolling heavy thin disks along rotate curvilinear line and energy analysis

Construction of the phase trajectory portraits of a generalized rolling pendulum along rotate curvilinear line is presented. The generalized rolling pendulum containing a rolling thin heavy disk rotates along the curvilinear line consisting of three circle arches, with constant angular velocity around a vertical eccentric/central axis. Depending on system parameters, different possible forms of the phase portraits appear with different structures of the sets of singular points and forms of phase trajectories. Trigger of coupled singular points and homoclinic orbit in the form of deformed number “eight” appears. A mathematical analogy between nonlinear differential equations of the considered generalized rolling pendulum and motion of the heavy mass particle along rotate curvilinear line, which are same form, is pointed out. On the basis of the obtained different possible phase trajectory portraits, nonlinear phenomena in vibro-impact dynamics of two rolling thin disks on rotate curvilinear line are investigated. Energy transfer between rolling disks in each of the series of successive collisions is analyzed and presented on relative mechanical energy portraits for dynamics of each of the rolling disks in collision.