 A plausible answer lies in a difference in their views as to the degree and way in which physical nature forms a closed system. Descartes held that quantity of motion, conceived as the product of speed and bulk, is conserved in all physical  interactions.[2]  This view allowed him to hold that mental substances can interact with bodies and influence their motions, so long as they influence only their direction. But given such influence, there can be no fully general physical laws covering collisions. The precise state of a physical system for Descartes cannot be determined by its prior state plus the laws of  nature.[3]  In this sense Descartes was not a physical determinist. Given that the possible intrusion of extra-physical influence precludes fully general collision laws, Descartes might not have thought it worthwhile to puzzle too much over the formulation of laws concerning non-linear motion, thinking it sufficient to illustrate the application of the principles governing interaction only in the simplest cases.