The trifilar pendulum is a well-known and established technique for the measurement of the moment of inertia of rigid bodies. For such application, the motion off the pendulum, which is inherently nonlinear, is considered linear. As consequences, only small oscillations and pendula with long cables with respect to their distance should be employed for the measurement. However, in some application either to use non- small oscillation angles or to use pendulum with relative short cables have to be employed. In these cases, the motion cannot be considered linear and some error in the measurement could arise. 

This paper aims to analyze the nonlinear motion off the pendulum. A formula is analytically derived for the calibration of the pendulum for non-small rotation angles. A sensitivity analysis is proposed to highlight the advantages of the proposed approach to the measurement of the moment of inertia of relatively smalll and compact bodies, such as tires and engines, and to full scale vehicles and airplanes.

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