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The sudden unbalanced short circuit of the 3-phase synchronous machine constitutes one of the most difficult problems of conventional machine analysis, whether traditional or unified. It is, however, readily susceptible to numerical integration using digital computers. The general approach, which is believed to have a wide application, is illustrated by the simple case of the 2-winding single-phase machine, and is then extended to the practical problem of the salient-pole machine with damper windings. Predicted and test results are found to be in good agreement.