http://www.unc.edu/~mgood/research/Goldstein_13_14.pdf [Broken] The problem is 2.14 in the link above. I have some trouble understanding the approach with Lagrangian multipliers. What are the idea of them? It seems you introduce them to have the freedom to vary your other degrees of freedom independently - is that correctly understood? So in the problem with the hoop ρ = r +R and θ (angle from vertical to the mass) are not really independent since at some point the hoop will roll of but you make them independent by introducing these multipliers. Is that how I should understand it? Also my specific problem is that I don't understand the expression for the kinetic energy in the solution. I can understand the terms ½m[itex]\rho[/itex]'2 and ½mr2[itex]\phi[/itex]'2. But how do you come the term ½m[itex]\rho[/itex]'2θ'2? Since v=rθ' should we have this term to be ½mr2θ'2?