Method of deriving equations of motion for dynamically adjustable gyroscope

The equations of motion for a dynamically adjustable gyroscope are derived in terms of the Lagrange function, of generalized coordinates and velocities and of time, this function assumed to be analytic. The derivation is based on applying an Euler operator to the corresponding Lagrange equation of the second kind and analyzing the Lagrange function as the difference between kinetic energy and potential energy. Linear differential equations of motion are derived in this way, first for a gyroscope with single wheel and then for one with n wheels in tandem. The method is also applicable to derivation of linearized nonlinear equations or their higher-order approximations.