Six illustrations of curl force dynamics

Curl forces, generating accelerations that are not the gradients of potentials, are a recent extension of Newtonian dynamics. The characteristic feature is that the dynamics is both nonconservative and nondissipative. This is illustrated visually for a series of forces, constituting a hierarchy of increasing richness. Starting with a separable Hamiltonian that is not a curl force, the hierarchy continues with a curl force described by an integrable Hamiltonian, a curl force described by a nonintegrable Hamiltonian, a separable non-Hamiltonian curl force, a nonseparable curl force not described by a Hamiltonian, and the culmination: a curl force for which there are no conserved quantities—a unique dynamical phenomenon. The pictures are easy to generate, and could be developed in several directions as student projects.