Geometric Analysis of Hamiltonian Mechanics using Connections

This contribution tries to clarify the role of connections in mechanics. From a geometric point of view connections appear naturally in an intrinsic description of mechanics, such that the equations remain their structure, even though time dependent transformations are applied. The choice of connections is of course not unique and physical considerations are essential for the proper selection. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)