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A ROUTE TO ROUTH — THE CLASSICAL SETTING

There is a well known principle in classical mechanic stating that a variational problem independent of a configuration space variable w (so called cyclic variable), but dependent on its velocity w' can be expressed without both w and w'. This principle is known as the Routh reduction. In this paper, we start to develop a purely geometric approach to this reduction. We do not limit ourselves to rather special problems of mechanics and in a certain sense we are able to obtain explicit formulae for the reduced variational integral.