Extremal Principles in Mechanics

Here we will present a most simple tool that will offer more certainty to decide in between possible reaction mechanisms of degradation, apart from the pure intuition. The starting point is the mechanics of a system. It is well established that the mechanical equilibrium is associated with a minimum of energy. There is a complete analogue to chemical equilibrium. 

Crossing over from mechanical and chemical equilibrium to kinematics in mechanical sciences and to kinetics in chemistry the analogy is not established as well. Descriptive chemical kinetics is a very different concept than the concept of kinematics. Kinematics is governed by the Hamiltonian equations or other extremal principles. 

A simple procedure to calculate the energies of the intermediates in a complex chemical degradation along the reaction coordinate, using the method of increments by van Krevelen, will be developed. From the energies along the reaction coordinate we will discriminate among various proposed reaction mechanisms. 

The equilibrium of mechanical systems and chemical systems is described just in the same way. The concept of virtual work can be applied in both cases successfully to obtain the equilibrium state. 

The path of mechanical systems has been described by extremal principles. We emphasize the principles of Fermat Hamilton. The principle of least action is named after Maupertui but this concept is also associated with Leibnitz, Euler, and Jacobi For details, cf. any textbook of theoretical physics, e.g., the book of Lindsay [16, p. 129]. Further, it is interesting to note that the importance of minimal principles has been pointed out in the field of molecular evolution by Davis [17]. So, in his words 

---