I was thinking up a problem today, and am unsure how to solve it.
Let's say we have a surface modeled by $g(x,y,z) $, where $z $ is the height from the lowest point, which we will set as $z = 0$. We place a golf ball of mass $m $ at the location $(x,y,z) = (x_0,y_0,z_0) $ on the surface. Find the function, $f$, which gives you the location of the ball at a specified time, where the ball is subject to a gravitational field.
thoughts:
My idea was that we cold possibly use Lagrange Multipliers and/or the Euler equation, however I'm unsure how to do it if this is possible (I am very new to these concepts, and have yet to see how they relate).
As $t \to \infty $, the ball will be at rest at the location of a minimum for $g (x,y,z) $.