Newton’s laws of motion in the form of a Riccati equation

2001/10/31 by M. Nowakowski, H. C. Rosu · 3 citations
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #physics.class-ph

paper · pdf · doi:10.1103/physreve.65.047602

published as Phys.Rev. E65 (2002) 047602 · 4 pages, twocolumn, accepted at Phys. Rev. E (2002)

arxiv created 2002/01/18 · openalex publication_date 2002/03/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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(r)=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.

Citations

• Supersymmetry and Quantum Mechanics

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