1.
Phys Rev E Stat Nonlin Soft Matter Phys
; 65(4 Pt 2B): 047602, 2002 Apr.
Artigo
em Inglês
| MEDLINE
| ID: mdl-12006083
RESUMO
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.