We discuss two applications of a Riccati equation to Newton’s laws of motion. The first one is the motion of a particle under the influence of a power law central potential ${V\left(r\right)=kr}^{\epsilon }.$ For zero total energy we show that the equation of motion can be cast in the Riccati form. We briefly show here an analogy to barotropic Friedmann-Robertson-Lemaitre cosmology where the expansion of the universe can be also shown to obey a Riccati equation. A second application in classical mechanics, where again the Riccati equation appears naturally, are problems involving quadratic friction. We use methods reminiscent to nonrelativistic supersymmetry to generalize and solve such problems.

• Received 12 October 2001

DOI:https://doi.org/10.1103/PhysRevE.65.047602