Three Faces of Mechanics

Newtonian, Lagrangian, and Hamiltonian Mechanics Newtonian, Lagrangian, and Hamiltonian mechanics are three different formulations of classical mechanics. They describe the same physical motion, but use different mathematical quantities and approaches to determine how a system evolves. Newtonian mechanics: focuses on forces and acceleration. Lagrangian mechanics: focuses on kinetic energy, potential energy, and the principle of stationary action. Hamiltonian mechanics: focuses on position, momentum, and the total energy expressed as a function of these variables. Let's examine each formulation and then apply all three to the same physical example.