(2026) 6, pp. 141-176. (pdf)
Thad S. Morton
Abstract:
Rotor imbalance is derived from kinetic energy without prescribing centrifugal forces. A temporal SE(3) velocity generator produces a single kinetic energy integral whose expansion reveals the zeroth, first, and second mass moments governing translation, translation-rotation coupling, and rotation. These moments form a homogeneous mass-moment matrix from which the conventional inertia matrix and parallel-axis theorem are recovered. Differentiation of kinetic energy with respect to the temporal generator yields a unified momentum wrench containing linear and matrix angular momenta. Applications to an eccentric rigid rotor and a flexible-shaft Jeffcott rotor demonstrate how rotating forces, moments, and shaft whirl follow from the underlying mass distribution, including rotor bore offsets, eccentric masses, and misaligned axes. The formulation connects rotor imbalance and shaft response without requiring the manual gathering of relevant terms.
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