1. The problem statement, all variables and given/known data A particle is conﬁned to move on the surface of a circular cone with its axis on the vertical z axis, vertex at origin (pointing down), and half-angle α(alpha) a) write down the lagrangian in terms of spherical coordinates r and ø (phi) 2. Relevant equations x=rsinθcosø y=rsinθsinø z=rcosθ the constraint for a circular cone is z=( x^2 + y^2)^1/2 3. The attempt at a solution So using this constraint and some definitions of cartesian--> spherical coordinates one can show that θ is constant, i.e θ=α (alpha) My problem here is setting up the Kinetic Energy, as the Lagrangian (L) is L= T (kinetic) - U(potential) energies. In cartesian T= 1/2m(d/dt(x)^2+d/dt(y)^2+d/dt(z)^2) My problem is now converting this to spherical polar coordinates, keeping in mind all time derivatives of θ=zero because theta is constant (θ=α) I've found a solution online and it gives the kinetic Energy as T=1/2m(d/dt(r)^2+(rsinαø^(dot))^2) ...so the 1/2m( rdot^2 + (rsinαø(dot)^2) where ø(dot) is time derivate w.r.t phi...If anyone could help me get to this conclusion it would be appreciated. I've tried substituting directly for d/dt (x^2+y^2+z^2) but i do not get this answer, i think it is just perhaps my math (algrebra) screwing me up. Thanks in advance.