A Force is called conservative iff , where


For a Force with no dependency on the velocity , Total Energy is constant only if the Force is conservative


A force is conservative iff the partial derivatives commute

is a conservative force iff for the domain of , where


If is conservative, . Hence

Conversely, If satisfies we can use path integrals to define , and use Stokes theorem to show that the integral is independent of the choice of paths.

  • Rename the result above and move it to it’s own note.