Nonlinear model of a pendulum-variable reluctance AC bridge velocity gauge

A theoretical model is developed for a pendulum-variable inductance ac RL bridge type velocity gauge. Lagrange´s equations and an extension of a solution to a restricted form of Navier-Stokes´ equations are used to develop the mechanical-fluidic portion of the model. Ampere´s circuital law and Kirchhoff´s laws are the basis for the magnetic-electrical portion of the model. State variables are defined and the overall model state equations written. A computer simulation of the model compares favorably with experimental results for the unforced case. The simulation also illustrates nonlinear damping effects as well as maximum and linear operating ranges for the gauge.