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
DOI:    460 Downloads     4671 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. Volume 1, Issue 2, December 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