Jacobi Stability of Circular Orbits in a Central Force

Abolghasem, Hossein

doi:10.1080/1726037X.2012.10698621

Open Access Original Articles

Jacobi Stability of Circular Orbits in a Central Force

Hossein Abolghasemhabolgha@stfx.caDepartment of Information SystemsSt. Francis Xavier UniversityAntigonish, Nova Scotia, B2G 2W5, CanadaView full profile →

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pp. 197–214Vol. 10Issue 2November 2012DOI: 10.1080/1726037X.2012.10698621XML

Received:: 28 Jun 2012
Accepted:: 21 Oct 2012
Published Online:: 03 Jun 2013
Article type:: Original Articles
Language:: EN
Article no.:: 1726037X.2012.10698621
Pages:: 197–214

Abstract

We examine the stability of circular orbits in a central force field from the Jacobi stability point of view (the KCC theory) and assert that condition for Jacobi stable circular orbits is the same known classical Liapunov stability criteria.

Keywords

Dynamical Systems Liapunov Stability Jacobi Stability KCC Theory Central Force

References

Abolghasem, H.2012 . Liapunov Stability Versus Jacobi Stability . , 10 ( 1 ) : 13 – 32 .
Antonelli, P.L.1993 . , 52 : 27
Antonelli, P.L.2000 . , Encyclopedia of Mathematics Dordrecht: Kluwer Academic Publishers .
Antonelli, P.L. and Bucataru, I.2001 . New results about the geometric invariants in KCC-theory . , 47 : 405 – 420 .
Antonelli, P.L., ed. 2003 . , Vol. 1 , Dordrecht: Kluwer Academic .
Arnold, V.I.1989 . , second , Springer .
Balan, V. and Nicola, I.R.2009 . Berwald-Moor metrics and structural stability of conformally-deformed geodesic SODE . , 11 : 19 – 34 .
Bao, D., Chern, S.S. and Shen, Z.2000 . , Springer .
Betounes, D.2010 . , second , Springer .
Boehmer, C.G. and Harko, T.2009 . Preprint math-ph/arXiv:0902.1054v4
Cartan, E.1933 . , 37 : 619
Chern, S.S.1939 . , 63 : 206
Goldstein, H., Poole, C. and Safko, J.2002 . , third , Addison Wesley .
Hale, J. and Kocak, H.1991 . , Springer-Verlag .
Kosambi, D.D.1933 . , 37 : 608
Perko, L.2006 . , third , Springer .
Rund, H.1959 . , Springer-Verlag .
Sabau, S.V.2005 . Some remarks on Jacobi stability . , 63 : 143
Harko, T. and Sabau, V.S.2008 . Jacobi stability of the vacuum in the static spherically symmetric brane world models . , 77 ( 10 ) : 104009
Boehmer, C.G., Harko, T. and Sabau, S.V.2010 . Preprint: math-ph/arXiv:1010.5464
Wiggins, S.1997 . , third , Springer-Verlag .

Views: 47Downloads: 64Citations: 14

[1] Abolghasem, H.2012 . Liapunov Stability Versus Jacobi Stability . , 10 ( 1 ) : 13 – 32 .

[2] Antonelli, P.L.1993 . , 52 : 27

[3] Antonelli, P.L.2000 . , Encyclopedia of Mathematics Dordrecht: Kluwer Academic Publishers .

[4] Antonelli, P.L. and Bucataru, I.2001 . New results about the geometric invariants in KCC-theory . , 47 : 405 – 420 .

[5] Antonelli, P.L., ed. 2003 . , Vol. 1 , Dordrecht: Kluwer Academic .

[6] Arnold, V.I.1989 . , second , Springer .

[7] Balan, V. and Nicola, I.R.2009 . Berwald-Moor metrics and structural stability of conformally-deformed geodesic SODE . , 11 : 19 – 34 .

[8] Bao, D., Chern, S.S. and Shen, Z.2000 . , Springer .

[9] Betounes, D.2010 . , second , Springer .

[10] Boehmer, C.G. and Harko, T.2009 . Preprint math-ph/arXiv:0902.1054v4

[11] Cartan, E.1933 . , 37 : 619

[12] Chern, S.S.1939 . , 63 : 206

[13] Goldstein, H., Poole, C. and Safko, J.2002 . , third , Addison Wesley .

[14] Hale, J. and Kocak, H.1991 . , Springer-Verlag .

[15] Kosambi, D.D.1933 . , 37 : 608

[16] Perko, L.2006 . , third , Springer .

[17] Rund, H.1959 . , Springer-Verlag .

[18] Sabau, S.V.2005 . Some remarks on Jacobi stability . , 63 : 143

[19] Harko, T. and Sabau, V.S.2008 . Jacobi stability of the vacuum in the static spherically symmetric brane world models . , 77 ( 10 ) : 104009

[20] Boehmer, C.G., Harko, T. and Sabau, S.V.2010 . Preprint: math-ph/arXiv:1010.5464

[21] Wiggins, S.1997 . , third , Springer-Verlag .

Journal of Dynamical Systems and Geometric Theories

WoS JIF 2026 : 0.5 (Q3)

Jacobi Stability of Circular Orbits in a Central Force

Abstract

Keywords

References