Classification of curl forces for all space dimensions

We present a decomposition of classical potentials into a conservative (gradient) component and a non-conservative component. The latter generalizes the curl component of the force in the three-dimensional case. The force is transformed into a differential $1$-form, known as the work form. This work form is decomposed into an exact (gradient) component and an antiexact component, which in turn generalizes the curl part of the force. The antiexact component is subsequently decomposed using the Frobenius theorem. This local decomposition is a useful tool for identifying the specific components of classical potentials.