Displaying similar documents to “Higher order almost tangent geometry and non-autonomous Lagrangian dynamics”

Sprays and homogeneous connections on 𝐑 × 𝑇𝑀

Alexandr Vondra (1992)

Archivum Mathematicum

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The homogeneity properties of two different families of geometric objects playing a crutial role in the non-autonomous first-order dynamics - semisprays and dynamical connections on R × T M - are studied. A natural correspondence between sprays and a special class of homogeneous connections is presented.

On naturality of the Helmholtz operator

Włodzimierz M. Mikulski (2005)

Archivum Mathematicum

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We deduce that all natural operators of the type of the Helmholtz map from the variational calculus in fibered manifolds are the constant multiples of the Helmholtz operator.

On Galilean connections and the first jet bundle

James Grant, Bradley Lackey (2012)

Open Mathematics

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We see how the first jet bundle of curves into affine space can be realized as a homogeneous space of the Galilean group. Cartan connections with this model are precisely the geometric structure of second-order ordinary differential equations under time-preserving transformations - sometimes called KCC-theory. With certain regularity conditions, we show that any such Cartan connection induces “laboratory” coordinate systems, and the geodesic equations in this coordinates form a system...