• Corpus ID: 56054530

Complete decoupling of systems of ordinary second-order differential equations

@inproceedings{Sarlet1997CompleteDO,
  title={Complete decoupling of systems of ordinary second-order differential equations},
  author={W. Sarlet},
  year={1997}
}

• W. Sarlet
• Published 1997
• Mathematics

A theory is presented leading to a geometric characterization of separable systems of second-order ordinary differential equations. The idea is that such a characterization should provide necessary and sufficient conditions for the existence of coordinates, with respect to which a given system decouples. The specific problem of decoupling is merely chosen as a motivation to review differential geometric tools for the description of second-order dynamical systems. In particular, a survey is presented of the theory of derivations of scalar and vector-valued forms along the projection of the velocity-phase space onto the configuration manifold. It is explained how this theory relates to the more traditional calculus on tangent or first-jet bundles. In discussing this relation, the geometrical objects which are important for studying separability or other features of the evolution of second-order dynamics, come forward in a natural way. A few other applications of this theory are briefly touched upon. ∗The subject which is being reviewed here concerns mainly joint work to which the following people have contributed: F. Cantrijn, J.F. Carinena, M. Crampin, E. Martinez, A. Vandecasteele. We acknowledge support by a NATO Grant (CRG 940195).