LOWERING THE ORDER OF EQUATIONS OF GYROSCOPIC SYSTEMS (O PONIZHENII PORYADKA URAVNENII GIROSKOPICHESKIKH SISTEM),
FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OHIO
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The possibility of reducing the order of gyroscopic equations is discussed. This is achieved by using a differential equation with a small parameter in its leading derivative. For a steady holonomic system the governing equation of motion for the gyroscope system is reduced by using the small parameter assumption mu lambda squared. Physically, this is equivalent to assuming the high frequency components of the motion to have a small period compared with its precession period. Two examples are given to illustrate the method. The first deals with the motion of a holonomic and scleronomic system under gyroscopic and dissipative forces. The second is the motion of a gyroscope with a universal joint of finite rigidity.