Semisprays, connections and regular equations in higher order mechanics. (English) Zbl 0809.58015

Vondra, Alexandr

Janyška, Josef (ed.) et al., Differential geometry and its applications. International conference, Brno, Czechoslovakia, 27 Aug. - 2 Sept. 1989. Singapore: World Scientific. 276-287 (1990).

Semisprays are second order differential fields. For such fields a relevant problem is to give a Lagrangian representation, i.e. to find a corresponding connection and a Lagrangian such that its extremals are the paths of the connection. Difficulties arise with unicity if symplectic forms are replaced by presymplectic forms. Therefore, as a generalization of second order differential fields, the author introduces a notion of semispray (and its paths) on fibred manifolds in such a way that the usual results still can be obtained.
For the entire collection see [Zbl 0777.00040].

Reviewer: B.Fuchssteiner (Paderborn)

MSC:

37J99

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems

Keywords:

second order differential fields; Lagrangian