# Is it true that an object, in course of its motion, always seeks the position of minimum potential energy?

I have heard the statement, in a Classical mechanics course, that the motion of an object is always toward the position of minimum potential energy. I don't think that this statement correct because I can immediately think of a counter-example. Consider the swing of the bob of a pendulum from the lowest position to one extreme position. During this part of its trajectory, the bob is moving to positions of higher potential energy than the minimum (at the lowest point) due to inertia.

Am I correct? Isn't this statement wrong?

$$\mathbf F = -\nabla V$$
In the generality that you stated it, this statement is false. What is true is that on an object always acts a force $F = - \nabla \Phi$ that is the gradient of the Potential. For an object at point $\vec{p}$, the negative gradient points towards a local minimum of the potential. This minimum isn't neccesarily the nearest minimum of the potential, and it's not even given that the potential has a minimum.