Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Newton's laws of motion in form of Riccati equation   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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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: math
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas