  A theory of double affine and special double affine bundles, i.e.
differential manifolds with two compatible (special) affine bundle structures,
is developed as an affine counterpart of the theory of double vector bundles.
The motivation and basic examples come from Analytical Mechanics, where double
affine bundles have been recognized as a proper geometrical tool in a
frame-independent description of many important systems. Different approaches
to the (special) double affine bundles are compared and carefully studied
together with the problems of double vector bundle models and hulls, duality,
and relations to associated phase spaces, contact structures, and other
canonical constructions.
