This might be a good place to start:PhilipsPhysics said:
Hamilton's Principle is a fundamental principle in classical mechanics that states that the path taken by a system between two points in time is the one that minimizes the action, which is the integral over time of the difference between the kinetic and potential energy of the system.
Hamilton's Principle was first proposed by Irish mathematician and physicist William Rowan Hamilton in the 19th century. However, it was later refined and popularized by French mathematician Joseph-Louis Lagrange.
Hamilton's Principle is significant because it provides a powerful and elegant framework for understanding and predicting the behavior of physical systems. It is also the basis for the powerful mathematical formalism of Lagrangian mechanics, which is widely used in modern physics.
Hamilton's Principle was derived from the principle of least action, which was first proposed by French mathematician Pierre-Louis Maupertuis in the 18th century. Hamilton built upon this principle and developed his own version, which is now known as Hamilton's Principle.
Hamilton's Principle is applied in various fields of science, including classical mechanics, quantum mechanics, and electromagnetism. It is used to derive the equations of motion for physical systems and to study the dynamics of complex systems. It is also used in the development of new theories and models in physics.