# American Institute of Mathematical Sciences

2009, 2009(Special): 191-197. doi: 10.3934/proc.2009.2009.191

## Spiral motion in classical mechanics

 1 Departamento de Ciencias Básicas, UAM-Azc., Av. San Pablo 180, Col. Reynosa, México D. F. 02200, Mexico 2 San Antonio 64, Col. Las Fuentes, Zapopan, Jalisco, 45070, Mexico

Received  October 2008 Revised  February 2009 Published  September 2009

We present various models in classical mechanics which exhibit 'exotic' orbits. We give an example of a smooth $|\mathbf{r}|$-independent potential
$V$ in dimension three, which exhibits an orbit that spirals as time goes to infinity. This kind of orbits cannot occur for this class of potentials in dimension two [4] or, see below, if ${Cr}=\{\omega\in S^{n-1}:\nabla V(\omega)=0\}$, $n\geq 3$, is totally disconnected. In addition, for each $\mu>2$ we give an example of a potential of the form $V(r,\theta)=O(r^{-\mu})$, in two dimensions, which is not radially symmetric and has a zero-energy orbit that escapes towards infinity in spirals. Zero energy orbits escaping towards infinity in spirals cannot occur for radial potentials with the same rate of decay.
Citation: Jamie Cruz, Miguel Gutiérrez. Spiral motion in classical mechanics. Conference Publications, 2009, 2009 (Special) : 191-197. doi: 10.3934/proc.2009.2009.191
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