The Dynamic Motion of a Missile Descending Through the Atmosphere

Abstract

A method is presented for computing rapidly, yet accurate^, the dynamic motion of a ballistic-type missile descending through the atmosphere. The equations of motion are separated into a set of static trajectory equations (zero angle of attack) and a set of equations describing the oscillatory motion of the missile about its center of gravity. A transformation allows the rotational equations to be written in a manner analogous to the equation for an undamped oscillating spring mass system with the mass equal to unity and a time variable spring constant. For given initial conditions this equation can be solved to obtain the envelope of maximum angle of attack. An additional transformation allows the calculation of the complete oscillatory motion at any time during the trajectory as a function of the maximum angle of attack at that time. This solution shows that the maximum angle of attack of a missile descending through the atmosphere at relatively constant speed is reduced even when the aerodynamic damping is neglected.