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Potential energy

Instead of a force, often the mathematically related concept of a potential energy field is used. For instance, the gravitational force acting upon an object can be seen as the action of the gravitational field that is present at the object's location. Restating mathematically the definition of energy (via the definition of work), a potential scalar field U (r) {\displaystyle U(\mathbf {r})} is defined as that field whose gradient is equal and opposite to the force produced at every point: F = − ∇ U. {\displaystyle \mathbf {F} =-\mathbf {\nabla } U.}

Forces can be classified as conservative or nonconservative. Conservative forces are equivalent to the gradient of a potential while nonconservative forces are not.