I believe the constraining equation is 0 = f(x) - y and that the condition when the bead leaves the surface is a condition which cause it not to be true. Using that constraining equation, I think the new Lagrangian would be L=.5*m*((dx/dt)^2)+((dy/dt)^2)+m*g*f(x)-k(f(x)-y) where k is the...
Homework Statement
An object of mass m, and constrained to the x-y plane, travels frictionlessly along a curve f(x), while experiencing a gravitational force, m*g. Starting with the Lagrangian for the system and using the method of Lagrange multipliers, derive the equations of motion for the...
A problem on an assignment I'm doing deals with a cart of mass m1 which can slide frictionlessly along the x-axis. Suspended from the cart by a string of length l is a mass m2, which is constrained to move in the x-y plane. The angle between the pendulum and vertical is notated as phi. The...