In this paper, transient and steady state behavior of Weakly Coupled Non-Linear Gyroscopic Systems response, amplitude and frequency of oscillation as well as stability properties have been studied in detail. The method adopted for analysis is based on multiple time perturbation approach. | Journal of Automation and Control Engineering Vol. 5, No. 1, June 2017 Multiple Time Analysis of Weakly Coupled Non- linear Gyroscopic Systems Shailendra Kumar Mittal Elect. Engg. Dept., G. H. Raisoni Institute of Engg. & Tech., Pune (.), India Email: mittalsai@, shailendramittal5@ supported by a asymmetric bearing Fedorchenks (1958, 61) analyzed the motions of gyroscopes resting on vibrating supports. Danby (1964), Grevinikov (1964), Alfriend (1970), Nayfeh and Mamel (1970) and Nayfeh (1970a) analyzed the stability of triangular points in the elliptic restricted problems of three bodies. Balachandra(1976) presented a survey of non-linear gyroscopic systems. The motion of general gyroscopic systems was studied by Cherry (1924), Moser (1958), Bert (1961), Arnold (1963), Butenin (1965, Hori (1966), Alfriend and Richardson (1973), Balachandra (1973), Sethna and Balachandra (1974), Ranga-charyayulu and Srinivasan (1973), Bhansali and Thiruvenkatchar (1975). Junkins, Jacobson and Blanton (1973) reduced the motion of any torque free rigid bodies to the solution of three uncoupled Duffing equations. Goodstain (1959) studied the free and forced vibrations of gyroscope. Throne (1961) solved numerically the equation governing the motion of gyroscopic under constant acceleration and correcting torque and Poli and Budrynes (1971) studied the symmetric gyroscope. Tiwari [1], [2] has considered higher order Non-linear system under free and forced condition and has established conditions for existence of limit cycle forced synchronized vibrations (both weak and strong forcing) for large number of classes of third order systems. Parametrically excited second orders as well as third order single degree of freedom systems have also been investigated for sustenance of Limit cycles. Singh [3] has considered the analysis of coupled nonlinear system under autonomous conditions using Multiple Time Scaling Technique. Linkein [4] have cited a very interesting .
