Hamilton’s Principle

Hamilton’s Principle 

Photo by Anoushka Puri on Unsplash

In the blog post, I discussed the Generalized coordinates and the need for Hamiltonian and Lagrangian.

Everything in the universe tends to stay in the ground state. All atoms, electrons, for example. This is because the minimum energy is the most stable state of the system. Here the energy is minimum, and the time interval is minimum.

Hamilton’s Principle states that for a conservative holonomic dynamic system, the motion of the system from its position in configuration space at time t1 to its position at time t2 follows a path for which the action integral has stationary (minimum or maximum) value. 

                Or 

Of all the possible paths along which a dynamical system may move from one point to another in a given interval of time, the actual path followed will minimize the time integral of the difference between kinetic energy and potential energy. 

So we write Hamilton’s Principle in ordinary and Generalized form as,