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In recent years new interest in Cherenkov radiation has arisen based on progress in its new applications like biomedical imaging, photonic structures, metamaterials, and beam physics. These new applications require Cherenkov radiation theory of short bunches to be extended to rather more complicated media and structures than considered originally. We present a new general approach to the analysis of Cherenkov fields and loss factors for relativistic short bunches in arbitrary slow wave guiding systems. This new formalism is obtained by considering a general integral relation that allows calculation of the fields in the vicinity of the charge. The proposed approach dramatically simplifies simulations using analytical fields near the moving source of Cherenkov radiation.