2.1 Newtonian mechanics

By Newton’s second law, one can the derive the equations of motion to describe the path \(q\) of the particle.

\[ -\nabla V(q) =F(q) = m\cdot a = m \dot v(t) = m \ddot q(t), \]

where \(\nabla\) is the gradient operator.

How to get to a geometrical structure? A geometrical description?