Mathematical Modeling of The Vertical Launch and Operation of An Aircraft Missile Gyroscope

The vertical launch system has been widely adopted to land- and sea-based guided missile systems, because of its excellent operation flexibility, quick response capability and effective utilization of the space volume over the deck. In this paper the advantages and technical characteristics of the vertical missile launch systems are presented and it is analyzed a process of inclination (turning) with respect to a missile necessary for an entrance in guidance trajectory. Special emphasis is placed on the role of the gyroscopic control in maintaining stable angle motion during important phases of flight initiation.
A mathematical model is developed for the motion of a guided missile that takes place between vertical launch and turn on torque. The model considers the forces and moments acting on a missile control system, control forces generated by impulse thrusters, inertia conditions, mass change as a result of fuel depletion and location of points of application. In addition, the angular response of a three directional gyroscope subjected to fixed and linearly moving bases is mathematically represented with generalized coordinates.
The derived equations include extra damping and restoring moment due to aerodynamic pressure, gravitational effect of the ground terrain, and external disturbances. Both correctable and uncorrectable gyro spin configurations are examined, so that the model may be used over the full envelope of missile guidance platforms. The formulated identifiability conditions establish a solid foundation for the structure design, which can be incorporated in authors’ future research on intelligent missile control system algorithms to promote guidance accuracy, stability and survivability in the stages of vertical launch and initial maneuvering.