  The Tulczyjew triple on a principal bundle with connection is constructed in
a convenient trivialisation. A reduction by the structure group is performed
leading to the triple on the trivialised Atiyah algebroid and a presentation of
this algebroid via a double vector bundle morphism. The dynamics of physical
systems with configuration manifolds having the structure of a principal bundle
with connection or the Atiyah algebroid is discussed and applied to the example
of an axially symmetric body confined to a sphere.
