42
Views
15
CrossRef citations to date
0
Altmetric
Original Articles

Jacobi Stability of Circular Orbits in a Central Force

Pages 197-214 | Received 28 Jun 2012, Accepted 21 Oct 2012, Published online: 03 Jun 2013

References

  • Abolghasem , H. 2012 . Liapunov Stability Versus Jacobi Stability . Journal of Dynamical Systems & Geometric Theories , 10 ( 1 ) : 13 – 32 .
  • Antonelli , P.L. 1993 . Tensor N. S , 52 : 27
  • Antonelli , P.L. 2000 . Equivalence problem for systems of second-order ordinary differential equations , Encyclopedia of Mathematics Dordrecht : Kluwer Academic Publishers .
  • Antonelli , P.L. and Bucataru , I. 2001 . New results about the geometric invariants in KCC-theory . An.St. Univ. ”Al.I.Cuza” Iasi. Mat. N.S , 47 : 405 – 420 .
  • Antonelli , P.L. , ed. 2003 . Handbook of Finsler geometry , Vol. 1 , Dordrecht : Kluwer Academic .
  • Arnold , V.I. 1989 . Mathematical Methods of Classical Mechanics , second , Springer .
  • Balan , V. and Nicola , I.R. 2009 . Berwald-Moor metrics and structural stability of conformally-deformed geodesic SODE . Applied Sciences , 11 : 19 – 34 .
  • Bao , D. , Chern , S.S. and Shen , Z. 2000 . An Introduction to Riemann-Finsler Geometry , Springer .
  • Betounes , D. 2010 . Differential Equations: Theory and Applications , second , Springer .
  • Boehmer , C.G. and Harko , T. 2009 . Nonlinear stability analysis of the Emden-Fowler equation Preprint math-ph/arXiv:0902.1054v4
  • Cartan , E. 1933 . Math. Z , 37 : 619
  • Chern , S.S. 1939 . Bulletin des Sciences Mathematiques , 63 : 206
  • Goldstein , H. , Poole , C. and Safko , J. 2002 . Classical Mechanics , third , Addison Wesley .
  • Hale , J. and Kocak , H. 1991 . Dynamics and Bifurcations , Springer-Verlag .
  • Kosambi , D.D. 1933 . Math. Z , 37 : 608
  • Perko , L. 2006 . Differential Equations and Dynamical Systems , third , Springer .
  • Rund , H. 1959 . The Differential Geometry of Finsler Spaces , Springer-Verlag .
  • Sabau , S.V. 2005 . Some remarks on Jacobi stability . Nonlinear Analysis , 63 : 143
  • Harko , T. and Sabau , V.S. 2008 . Jacobi stability of the vacuum in the static spherically symmetric brane world models . Physical Review D , 77 ( 10 ) : 104009
  • Boehmer , C.G. , Harko , T. and Sabau , S.V. 2010 . Jacobi stability analysis of dynamical systems-applications in gravitation and cosmology Preprint: math-ph/arXiv:1010.5464
  • Wiggins , S. 1997 . Introduction to Applied Nonlinear Dynamical Systems and Chaos , third , Springer-Verlag .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.