Transient analysis of energy equation of dynamical systems

In the scope of numerical simulation, this report presents a method to evaluate the (t)u(t) Dirac product which is encountered when formulating energy equations of dynamical systems. A simple pendulum is taken as an example and its simulation scheme is designed. The transient analysis of the system driven by an impulse command is finally used to illustrate that (t)u(t) = 0:5 (t); a proof of such a result is also provided.