Classical Mechanics: Newton, Lagrange, Hamilton

This lecture delves into the fundamental principles of classical mechanics, exploring how to calculate particle positions over time by integrating equations of motion. The instructor explains Newton's laws, the potential energy function, and the challenges of analytically solving complex force equations. Additionally, the lecture introduces Lagrange's mechanics as a more general formulation, discussing generalized coordinates, Lagrange's equations, and the method of Lagrangian multipliers. The concept of Hamiltonian mechanics is also presented, focusing on canonical coordinates, the Hamiltonian function, and Hamilton's equations of motion. By comparing these three equivalent formulations, the lecture provides insights into different ways of describing classical dynamics.