@Hamilton’s variational principle & Lagrange’s equation of motion fromHamilton’s Principle
@Hamilton's variational principle, also known as Hamilton's principle or the principle of stationary action, is a fundamental concept in classical mechanics and the calculus of variations. It was developed by the Irish mathematician and physicist William Rowan Hamilton in the 19th century as a reformulation of the equations of motion in classical mechanics.
@Lagrange's equation of motion can be derived from Hamilton's principle by defining the Lagrangian, writing the action integral, applying Hamilton's principle to find the variation in the action, integrating by parts, and then setting the coefficient of the variation in the generalized coordinates to zero.