This paper is the first of a series whose purpose is to relax the usual assumptions in the analysis of shaft vibration. The formulation of a more complete theory suggests a method of balancing flexible shafts, a fresh approach to problems of stability and a way of allowing for bearing characteristics; it also suggests methods of allowing for lack of axial symmetry. Following a suggestion due to Johnson (1, 2)†, the theory is developed in simple terms. Use is made in this exposition of the mechanical analogy which exists between an initially bent shaft and a simple conical pendulum whose point of support is given a circular motion in a horizontal plane.
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