Coning motion of spinning missiles induced by the rate loop

Rate loops are commonly employed to compensate damping for missiles due to their great effectiveness. However, unexpected coning instability could be induced when the missile is subjected to spinning. The stability condition of coning motion as well as suitable design criteria for spinning missiles with rate loop feedback is established in this paper. Based on the theory of nutation movement, nonlinear equations of motion in terms of the nutation and precession angles are created. The mathematic model of the actuator acting on spinning missiles is also derived. After introducing the complex angle of attack into the system, the governing equations can be simplified to an analytically solvable second-order differential equation with respect to this variable. The proposed method is demonstrated by numerical simulations. It is also found that the upper limit of the critical gain in the damping loops' feedback for the stability decreases dramatically with a spinning missile. The dynamic inverse technique is employed as a remedy and it shows great effectiveness and applicability for the problem discussed in this paper.