Paper: On the Secular Evolution of Asteroids Volume: 107, Completing the Inventory of the Solar System Page: 69 Authors: Scherer, K.; Neutsch, W. Abstract: The evolution of asteroidal orbits under the secular perturbations of Jupiter is studied. The influence of Jupiter is calculated using the Gaussian secular perturbation method applied in a way such that the perturbing function can be calculated analytically. The remaining integration over the orbit uses the Runge--Kutta method operating on the angular momentum vector {$\,\vec{C}$} and the Runge--Lenz vector $\,\vec{A}$. The evolution of these two vectors is displayed in a stereographic projection in which the paths of these vectors evolve along characteristic epicycles. In this projection, the vectors of members of classical Hirayama families lie within small annuli and are nonuniformly distributed within these annuli. Moreover, the members of a family can be regarded as data" measured at different evolutionary times. Thus the orbits of these asteroids can be characterized by their evolutionary curves and the classical families understood as dynamical clusters in element space.