result, all superintegrable systems are automatically describable by Nambu mechanics, alternatively, and equivalently, to Hamiltonian mechanics. Maximally superintegrable systems can be quantized using commutation relations, as illustrated below. Nevertheless, equivalently, they are also quantized in the Nambu framework, such as this classical Kepler problem into the quantum hydrogen atom. Evolution under perturbed potentials The Laplace–Runge–Lenz vector A is conserved only for a perfect inverse-square central force. In most practical problems such as planetary motion, however, the interaction potential energy between two bodies is not exactly an inverse square law, but may include an additional central force, a so-called perturbation described by a potential energy . In such cases, the LRL vector rotates slowly in the plane of the orbit, corresponding to a slow apsidal precession of the orbit. By assumption, the perturbing potential is a conservative central force, which implies that the total energy and angular momentum vector L are conserved. Thus, the motion still lies in a plane perpendicular to L and the magnitude is conserved, from the equation . The perturbation potential may be any sort of function, but should be significantly weaker than the main inverse-square force between the two bodies. The rate at which the LRL vector rotates provides information about the perturbing potential . Using canonical perturbation theory and action-angle coordinates, it is straightforward to show that A rotates at a rate of, where is the orbital period, and the identity was used to convert the time integral into an angular integral (Figure 5). The expression in angular brackets, , represents the perturbing potential, but averaged over one full period; that is, averaged over one full passage of the body around its orbit. Mathematically, this time average corresponds to the following quantity in curly braces. This averaging helps to suppress fluctuations in the rate of rotation. This approach was used to help verify Einstein's theory of general relativity, which adds a small effective inverse-cubic perturbation to the normal Newtonian gravitational potential, Inserting this function into the integral and using the equation to express in terms of , the precession rate of the periapsis caused by this non-Newtonian perturbation is calculated to be which closely matches the observed anomalous precession of Mercury and binary pulsars. This agreement with experiment is strong evidence for general relativity. Poisson brackets The unscaled functions The algebraic structure of the problem is, as explained in later sections, SO(4)/Z2 ~ SO(3) ×