Open Access
Original Articles
Liapunov Stability Versus Jacobi Stability
Hossein Abolghasemhabolgha@stfx.caDepartment of Information Systems, St. Francis Xavier UniversityAntigonish, Nova Scotia, B2G 2W5, CanadaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 13 Jun 2011
- Accepted:
- 30 Mar 2012
- Published Online:
- 01 May 2012
- Article type:
- Original Articles
- Language:
- EN
- Article no.:
- 1726037X.2012.10698604
- Pages:
- 13–32
Abstract
Liapunov stability and Jacobi stability are based on two different concepts and methods. The stability of classical example of a torque-free rigid body motion around a stationary point has been examined from Liapunov stability and Jacobi stability (or KCC theory) viewpoints. Unlike some worked example investigated by other authors, where there are discrepancies between these two methods, our case here shows complete agreement between two methods.
Keywords
References
Antonelli, P.L.1993 . Tensor N. S., 52 ( 27 ) Antonelli, P.L.2000 . “ Equivalence problem for systems of second-order ordinary differential equations ” . In 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 . Boehmer, C.G. and Harko, T.2009 . Nonlinear stability analysis of the Emden-Fowler equationPreprint 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 Marsden, J.E. and Ratiu, T.S.1999 . Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems, second , Springer . 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 cosmologyPreprint: math-ph/arXiv:1010.5464 Siegel, C.L. and Moser, J.K.1971 . Lectures on Celestial Mechanics, Springer . Steigenberger, J. and Fliegner, T.1992 . Stability of a disturbance decoupled rigid body . Systems and Control Letters, 19 : 249 – 254 . Tu, Pierre N.1995 . Dynamical Systems: An Introduction with Applications in Economics and Biology, Springer-Verlag . Wiggins, S.1997 . Introduction to Applied Nonlinear Dynamical Systems and Chaos, third , Springer-Verlag .
Views: 12Downloads: 13Citations: 18
