Dynamic Modeling for Hemispherical Resonator Gyro by Using Lagrangian Mechanics

Abstract

As an essential element of inertial technology，hemispherical resonator gyro(HRG)has become a prior choice of space applications. Dynamic modeling for HRG is the foundation of explicit analysis for HRG’s the- pries. Based on LOVE’s basic hypothesis，harmonic oscillator can be treated as hemispherical elastic thin shell. Elongation and angle changes can be calculated by using elastic thin shell theory. Then the whole kinetic energy and potential energy can be calculated by using Lagrangian Mechanics，thus establishing the Lagrangian equations， as which consequence，the dynamic model of hemispherical harmonic oscillator is obtained. The result shows that the obtained model is equivalent to a 2一D simple harmonic vibration model of a mass block，as which result，the dy- namic model of HRG is simplified.

Keywords

• hemispherical resonator gyroscope; dynamic model; elastic thin shell; lagrangian mechanics