Advanced Search
Article Contents
Article Contents

Jacobi fields for second-order differential equations on Lie algebroids

Abstract Related Papers Cited by
  • We generalize the concept of Jacobi field for general second-order differential equations on a manifold and on a Lie algebroid. The Jacobi equation is expressed in terms of the dynamical covariant derivative and the generalized Jacobi endomorphism associated to the given differential equation.
    Mathematics Subject Classification: 34A26, 58Z05, 58Cxx.


    \begin{equation} \\ \end{equation}
  • [1]

    J. F. Cariñena and E. Martínez, Generalized Jacobi equation and Inverse Problem in Classical Mechanics, In Group Theoretical Methods in Physics II (Moscow 1990), Nova Science Publishers, New York, 1991


    J. Cortés, M. de León, J. C. Marrero and E. Martínez, Nonholonomic Lagrangian systems on Lie algebroids, Discrete and Continuous Dynamical Systems A, 24 2 (2009), 213-271doi: 10.3934/dcds.2009.24.213.


    M. Crampin and F. A. E. Pirani, Applicable Differential Geometry, Cambridge University Press, 1986


    M. de León, J. C. Marrero and E. Martínez, Lagrangian submanifolds and dynamics on Lie algebroids, J. Phys. A: Math. Gen., 38 (2005), R241-R308


    P. Foulon, Géométrie des équations différentielles du second ordre, Ann. Inst. H. Poincaré Phys. Théor., 45 (1986), 1, 1-28


    L. A. Ibort and E. Martínez, Morse theory for Lagrangian systems, Unpublished (1997)


    K. C. H. Mackenzie, General Theory of Lie Groupoids and Lie Algebroids, Cambridge University Press, 2005


    E. Martínez, Lagrangian Mechanics on Lie algebroids, Acta Appl. Math., 67 (2001), 295-320


    E. Martínez, Reduction in optimal control theory, Reports on Mathematical Physics 53 (2004), 79-90doi: 10.1016/S0034-4877(04)90005-5.


    E. Martínez, Classical field theory on Lie algebroids: variational aspects, J. Phys. A: Math. Gen., 38 (2005), 7145-7160doi: 10.1088/0305-4470/38/32/005.


    E. Martínez, Variational calculus on Lie algebroids, ESAIM: Control, Optimisation and Calculus of Variations 14 02, 2007, 356-380doi: 10.1051/cocv:2007056.


    E. Martínez, J. F. Cariñena and W. Sarlet, Derivations of differential forms along the tangent bundle projection. Part II, Differential Geometry and its Applications 3 (1993) 1-29


    P. W. Michor, The Jacobi flow, Rend. Sem. Mat. Univ. Politec. Torino 54 (1996), 365-372

  • 加载中
Open Access Under a Creative Commons license

Article Metrics

HTML views() PDF downloads(220) Cited by(0)

Access History



    DownLoad:  Full-Size Img  PowerPoint