Minimum Energy and Energy Dissipation Rate

The theory of minimum energy and the minimum rate of energy dissipation have been applied to flow around bluff bodies, stability of falling bodies, statics and dynamics of gas bubbles, generation of ripples and dunes, and drag reduction by suspended load. These examples are used to illustrate how the minimization principles (variational principles) can be used to solve the problems of dissipative mechanical systems in static or dynamic equilibrium conditions. The minimization principle can be used independently or in tandem with the equations of motion to solve problems of a large degree of freedom. The equilibrium solution thus obtained has been shown to contain certain implicit information on the stability characteristics of the equilibrium state. For this reason, the method is not only a viable alternative to the vector mechanics method, but it also provides a relatively simple way of determining certain stability criteria.