 Consider a particle moving under the influence of the central force, and let "h" be its specific angular momentum, then the particle moves along a Cotes's spiral, with the constant "k" of the spiral given by

when "μ" < "h"2 (cosine form of the spiral), or

when "μ" > "h"2, Poinsot form of the spiral.When "μ" = "h"2, the particle follows a hyperbolic spiral.The derivation can be found in the references.