A theoretical analysis of dynamic interactions between systems

Dynamic interactions between dynamic systems are analyzed theoretically. Specifically, three cases that the two systems are (1) isolated from each other, (2) in contact with each other, and (3) at the moment of colliding with each other are investigated in a systematically. The extended Hamilton´s principle is used as a principle of mechanics that governs the dynamic behaviors of the systems. Besides, it is assumed that the contact between the two systems can be represented by the classical nonholonomic constraint including the holonomic constraint as a special case. As a result, it is shown that the dynamic interaction can be described by the constraint on the generalized coordinates of the systems and the condition for the generalized forces of constraint. The dynamic interaction can also be expressed in terms of a particular block diagram accompanied with an inputting port of displacements and an outputting port of forces of constraint