01
Lagrangian
L = T - V
The Lagrangian is defined as kinetic energy minus potential energy for many standard mechanical systems.
02
Euler-Lagrange Equation
d/dt(∂L/∂q̇) - ∂L/∂q = 0
This equation produces the equations of motion while allowing generalized coordinates and constraints to be handled systematically.
03
Principle of Stationary Action
S = ∫ L dt
Classical trajectories can be characterized as paths for which the action is stationary under small variations, providing a powerful unifying formulation of mechanics.