# Sliding down a parabola.

1. Nov 23, 2008

### devon cook

1. The problem statement, all variables and given/known data
Honestly, this site is more complicated than the problem I'm trying to solve. Like ... everybody... I've changed the equation of the curve. Think simple!! A stupid bead slides down a parabola (y=(1/2)x^2 from x=1 to x=0 to the left, ok? I've done Lagrangian mechanics on it and got the DE
x''(1+x^2)+x(x')^2 +gx=0 !!! (The dash " ' " is with repect to time) . Let's say my maths is ok on that, right?
POINT 1. If you analyze it using Newtonian mechanics (according to me) the x(x') term is missing. That's not good. That's not even close to good.
POINT 2. I've solved this DE (x''(1+x^2)+x(x')^2 +gx=0 ) and got a function for the horizontal velocity in terms of distance which looks sensible.
BASICALLY!!! I just want some feedback here, coz it's interesting and I don't know if I'm right. Hey, you guys in the US or whatever, contact me.
Dev

2. Relevant equations

3. The attempt at a solution