A research on the electrostatic torques in the electrostatically suspended gyroscope (ESG) that uses the mass-unbalance modulation (MUM) scheme (MUM-ESG) to sense the direction of the rotor's spinning axis is pres...A research on the electrostatic torques in the electrostatically suspended gyroscope (ESG) that uses the mass-unbalance modulation (MUM) scheme (MUM-ESG) to sense the direction of the rotor's spinning axis is presented here. Spherical harmonic functions are used to describe the asphericity of the rotor and the electrodes. Rotational matrix theory in quantum mechanics is utilized to transform the description of the rotor's asphericity from the rotor-fixed frame into the cavity-fixed frame. And the principle of the virtual displacement is applied to find out the electrostatic torques acting on the rotor. Analytical expressions of the electrostatic torques indicate that there are only three kinds of factors need to be considered when looking for the electrostatic torques in the MUM-ESG. The factors are the asphericity of the rotor, the eccentric rotation of the rotor, and the coupling between the rotor's translational displacement and asphericity. An intuitionistic explanation for the electrostatic torque that comes of the rotor's eccentric rotation is presented also. The effects of these conclusions should be tested and verified in the future experiments and applications.展开更多
基金National Defense Pre-research Foundation of China(No.51409060104JW0307)
文摘A research on the electrostatic torques in the electrostatically suspended gyroscope (ESG) that uses the mass-unbalance modulation (MUM) scheme (MUM-ESG) to sense the direction of the rotor's spinning axis is presented here. Spherical harmonic functions are used to describe the asphericity of the rotor and the electrodes. Rotational matrix theory in quantum mechanics is utilized to transform the description of the rotor's asphericity from the rotor-fixed frame into the cavity-fixed frame. And the principle of the virtual displacement is applied to find out the electrostatic torques acting on the rotor. Analytical expressions of the electrostatic torques indicate that there are only three kinds of factors need to be considered when looking for the electrostatic torques in the MUM-ESG. The factors are the asphericity of the rotor, the eccentric rotation of the rotor, and the coupling between the rotor's translational displacement and asphericity. An intuitionistic explanation for the electrostatic torque that comes of the rotor's eccentric rotation is presented also. The effects of these conclusions should be tested and verified in the future experiments and applications.
