Derivation of the Equations of Motion Dynamics of Ring Wave Solid-State and Pendulum Gyroscopes by the Method of Holonomic Mechanics

A new view on the theory of the ring oscillator of a wave solid-state gyroscope is presented in the same formulation as [1], i.e., under the condition of inextensibility of the middle line of the ring.To obtain inertial information, the new physical principle introduced in [1] — the inert properties of elastic waves — is replaced by the principle of inertial motion of elastic deformations of the resonator, which are similar to the motions of liquid jets. This makes it possible to organize the modes of excitation and measurement of resonator oscillations based on Pascal's law: "The pressure applied to any part of liquid will be transmitted equally in all directions through the liquid."The inertial motions of elastic deformations of the resonator follow from the solutions of its equations. On the other hand, a strapdown inertial navigation system of the pendulum type is built on their basis.