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Movement is the primary reason for the existence of many electrical machines. Modeling movement can often be very expensive. In some circumstances where the moving object is invariant in the direction of motion, this approach can be simplified using methods, such as the Minkowski transform. In the general case, where the moving object is not as above, many solutions of nonlinear equations by time-stepping techniques can be required. Some methods developed in the past have stood the test of time and others have proved to be less useful.
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D. Rodger (2021) studied this question.
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