Theory and error analysis of vibrating-member gyroscope

A general method for investigating the errors in a vibrating-member gyroscope has been developed by first transforming the equations of motion from Cartesian coordinates to orbital elements and then transforming the resulting equations to linear, constant-coefficient equations in energy and angular momentum, after averaging over a cycle to more clearly exhibit the long term effects. The constant-coefficient system is solved in closed form for the individual effects of anisoelasticity and damping. The effect of nonlinear restoring forces is also studied. While these analyses cover the effects of principal sources of error, the method and general equations can also be used to study the effects of other errors.