Separability of time-dependent second-order equations

  • W. Sarlet
Part of the Mathematics and Its Applications book series (MAIA, volume 350)

Abstract

A theory is developed concerning the geometric characterization of separable systems of second-order ordinary differential equations. The idea is to find necessary and sufficient conditions which will guarantee the existence of coordinates, with respect to which a given system decouples. The methodology stems from the theory of derivations of scalar and vector-valued forms along the projection π0 1 : J1π → E, where E is fibred over R (projection π). Particular attention is paid to features of the time-dependent set-up, which differ from the previously developed theory for autonomous equations.

Keywords

Vector Field Tensor Field Linear Connection Horizontal Lift Autonomous Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    F. Cantrijn, W. Sarlet, A. Vandecasteele and E. Martínez: Complete separability of time-dependent second-order equations, preprint 1994.Google Scholar
  2. 2.
    M. Crampin, E. Martinez and W. Sarlet: Linear connections for systems of secondorder ordinary differential equations, preprint 1994.Google Scholar
  3. 3.
    A. Frölicher and A. Nijenhuis: Theory of vector-valued differential forms, Proc. Ned. Acad. Wetensch. Ser. A 59 (1956) 338–359.MATHGoogle Scholar
  4. 4.
    E. Martínez, J.F. Cariñena and W. Sarlet: Derivations of differential forms along the tangent bundle projection, Diff. Geometry and its Applications 2 (1992) 17–43.MATHCrossRefGoogle Scholar
  5. 5.
    E. Martínez, J.F. Cariñena and W. Sarlet: Derivations of differential forms along the tangent bundle projection II, Diff. Geometry and its Applications 3 (1993) 1–29.MATHCrossRefGoogle Scholar
  6. 6.
    W. Sarlet, A. Vandecasteele, F. Cantrijn and E. Martínez: Derivations of forms along a map: the framework for time-dependent second-order equations, Diff. Geometry and its Applications, (1994) to appear.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • W. Sarlet
    • 1
  1. 1.Theoretical Mechanics DivisionUniversity of GhentGhentBelgium

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