**General Mathematics, Vol. 5, No. 1 - 4, pp. 255-266, 1995 **

**Abstract:** Considering some regular geometric objects on the tangent and
cotangent bundles of a smooth manifold $M$, we define some diffeomorphisms between these
bundles, which establish some relations between the mechanical structures on $TM$ and
$T^{*}M$. We construct a mechanical structure on $T^{*}M$ and we also study the condition
under which a regular vector field defining a mechanical structure on $T^{*}M$ is a
semi-Hamilton or Hamilton vector field.

**Classification (MSC91):** 53C05, 53C15, 58F5.

**Keywords:** tangent and cotangent bundle, spray, regular vector field, nonlinear
connection, mechanical structure.

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