In this Letter we show that corrections to Newton's second law appear if we assume a symplectic structure consistent with the commutation rules of the non-commutative quantum mechanics. For central field we find that the correction term breaks the rotational symmetry. For the Kepler problem, this term is similar to a Coriolis force. © 2003 Elsevier Science B.V. All rights reserved.
Romero, J. M., Santiago, J. A., & Vergara, J. D. (2003). Newton’s second law in a non-commutative space. Physics Letters, Section A: General, Atomic and Solid State Physics, 310(1), 9–12. https://doi.org/10.1016/S0375-9601(03)00191-9