Milankovitch equations with spinors

We investigate the use of spinors to describe the secular evolution of quasi-Keplerian systems. Evaluating their Poisson brackets, we show that the components of a properly chosen spinor are canonical variables. We illustrate this formalism using the classical problems of the orbital motion about an oblate planet and the Kozai–Lidov mechanism. Although the present formalism breaks down for circular or radial orbits, it may be of some practical utility in numerical recipes.