Volume 1, Number 2 (2016)
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Home > Journals > SCIREA Journal of Physics > Archive > Paper Information

Noncircular orbits and organised chaos exemplified with sine circular map and Arnold's tongues.

Volume 1, Issue 2, December 2016    |    PP. 94-100    |PDF (398 K)|    Pub. Date: December 21, 2016
230 Downloads     1166 Views  

Author(s)
Lena J-T Strömberg, previously Sigma and Department of Solid Mechanics

Abstract
Assuming that time is determined by a present frequency, relations are derived based on the angular velocity of a noncircular orbit. Formats relating concepts of noncircular orbits with fix points of the sine circular map, so-called Arnold’s tongues, will be obtained.

Keywords
Avd, quantum chaos, frequency ratio, spatial ratio, angular velocity, sine circular map, Arnold’s tongues, fix points, noncircular orbits

Cite this paper
Lena J-T Strömberg, Noncircular orbits and organised chaos exemplified with sine circular map and Arnold's tongues., SCIREA Journal of Physics. Vol. 1 , No. 2 , 2016 , pp. 94 - 100 .

References

[ 1 ] Arnold V.I (1978). Mathematical Methods of Classical Mechanics (Graduate Texts in Mathematics, Vol. 60), Springer, 2nd Edition 1989.
[ 2 ] Ohlen G, Åberg S, Östborn P ( 2007). Chaos. Division of Mathematical Physics, LTH, 2007.
[ 3 ] Strömberg L (2014). A model for non-circular orbits derived from a two-step linearisation of the Kepler laws. Journal of Physics and Astronomy Research 1(2): 013-014.
[ 4 ] Strömberg L (2015). Motions for systems and structures in space, described by a set denoted Avd. Theorems for local implosion; Li, dl and angular velocities. Journal of Physics and Astronomy Research, 2(3): 070-073.
[ 5 ] [wik] https://en.wikipedia.org/wiki/Arnold_tongue

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