1. The problem statement, all variables and given/known data A particle of mass m slides frictionlessly down a smooth track defined by the function y=f(x)=((-x^3)/a^2) where a is a constant with units of length. The particle is also in a uniform gravitational field. Set the lagrangian up in cartesian coordinates x and y 2. Relevant equations L=T-U T=kinetic energy U=potential energy 3. The attempt at a solution Since L=T-U, I know the solution will looking something close to (1/2)m(x'^2+y'^2)=mg(f(x)) but I am having difficulty determining what my x and y should be so I can apply them to the equation. I assume y=((-x^3)/a) so would I just need to solve for x and say x=(-y*a^2)^(1/3) and differentiate both x and y to find my x' and y'.