Advanced Search
Article Contents
Article Contents

Spiral motion in classical mechanics

Abstract Related Papers Cited by
  • 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.
    Mathematics Subject Classification: Primary: 34C05, 37E35; Secondary: 70F99.


    \begin{equation} \\ \end{equation}
  • 加载中
Open Access Under a Creative Commons license

Article Metrics

HTML views() PDF downloads(123) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint