Main Question or Discussion Point
I have a bowl in the form of a parabola (say y=x^2, motion is in 2d! On the graph of the parabola) and i place an object on the edges of the bowl and let if fall in the bowl. I have gravity, and no friction. My question is plain simple: what are it's equations of motion? I know it has to oscillate. I know calculus quite well, but that doesn't seem to help. Is there something I'm missing out? I would simply love to see the correct equations :D. Thank you very, very much in advance.