Goldstein Classical Mechanics Solutions Chapter 4 __full__ Link

∂L/∂q - d/dt (∂L/∂q̇) = 0

U = (1/2)kr^2

A particle of mass m moves on a sphere of radius r under the influence of a force F = -k/r^2. Find the Lagrangian and the equations of motion. goldstein classical mechanics solutions chapter 4

Lagrangian mechanics is a reformulation of classical mechanics that uses the Lagrangian function, which is a combination of the kinetic energy and potential energy of a system. The Lagrangian function is used to derive the equations of motion, which describe the motion of a system. The Lagrangian approach is more general and more flexible than the Newtonian approach, and is widely used in many fields. ∂L/∂q - d/dt (∂L/∂q̇) = 0 U =

L = T - U = (1/2)m(ṙ^2 + r^2θ̇^2) - (1/2)kr^2 goldstein classical mechanics solutions chapter 4