dorsal/arxiv
View SchemaNewton's laws of motion in form of Riccati equation
| Authors | M. Nowakowski, H. C. Rosu |
|---|---|
| Categories | |
| ArXiv ID | physics/0110066 |
| URL | https://arxiv.org/abs/physics/0110066 |
| DOI | 10.1103/PhysRevE.65.047602 |
| Journal | Phys.Rev. E65 (2002) 047602 |
Abstract
We discuss two applications of 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 $V(r)=k r^{\epsilon}$. 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
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"abstract": "We discuss two applications of Riccati equation to Newton\u0027s laws of motion.\nThe first one is the motion of a particle under the influence of a power law\ncentral potential $V(r)=k r^{\\epsilon}$. For zero total energy we show that the\nequation of motion can be cast in the Riccati form. We briefly show here an\nanalogy to barotropic Friedmann-Robertson-Lemaitre cosmology where the\nexpansion of the universe can be also shown to obey a Riccati equation. A\nsecond application in classical mechanics, where again the Riccati equation\nappears naturally, are problems involving quadratic friction. We use methods\nreminiscent to nonrelativistic supersymmetry to generalize and solve such\nproblems",
"arxiv_id": "physics/0110066",
"authors": [
"M. Nowakowski",
"H. C. Rosu"
],
"categories": [
"physics.class-ph"
],
"doi": "10.1103/PhysRevE.65.047602",
"journal_ref": "Phys.Rev. E65 (2002) 047602",
"title": "Newton\u0027s laws of motion in form of Riccati equation",
"url": "https://arxiv.org/abs/physics/0110066"
},
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