(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I want to be able to plot a trajectory wrt time of a ball that rolls without slip on a curved surface.

Known variables:

-radius/mass/moment of inertia of the ball.

-formula for the curvature of the path (quadratic)

-formula relating path length and corresponding height above the ground. (linearly decreasing, i.e. as you travel down the curve, you decrease in height).

2. Relevant equations

Euler-Lagrange Equations

3. The attempt at a solution

See attached for further details.

I've come up with an answer for the acceleration of the ball along the path length. However, it isn't a function of the starting height as I expected. I suspect I may have made an assumption that I'm not supposed to but I can't see what it is.

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# Lagrangian Mechanics + Constraint: Trajectory of a rolling object on a curved surface

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