Derivation and Analysis of the Complete Nonlinear Dynamical Equations of the MICOM Stabilized Mirror System
ARMY MISSILE RESEARCH DEVELOPMENT AND ENGINEERING LAB REDSTONE ARSENAL AL GUIDANCE AND CONTROL DIRECTORATE
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The complete nonlinear dynamical equations of the MICOM stabilized mirror system mounted on a vehicle are derived and analyzed for certain stabilized motion. Lagranges formulation of DAlemberts principle is used to derive the highly coupled equations of motion of the gimballed platform, balancer, mirror, and azimuth and elevation gyroscopes. Four special cases of the full dynamical equations are presented. They are the equations based on the assumptions of a small vehicular motion, b small mass unbalance, c small deviations from system looking forward, and d both small motions and small mass unbalance. A block diagram is given for the analog simulation of case d. These equations are derived for the purposes of analyzing design changes in the basic structure and for designing stabilization and servo-control compensators for improved accuracy in tracking and stabilization. Although no new control system design is attempted, conclusions are drawn from the structure of the dynamical system equations.
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