The flight of a rocket vehicle in the equatorial plane of a rotating earth is considered with possible disturbances in the atllIosphere due to changes in density, in tellIperature, and in wind speed. These atllIospheric disturbances together with possible deviations in weight and in 1lI01lIent of inertia of the vehicle tend to change the flight path away frollI the norllIal flight path. The paper gives the condition for the proper cut-off tillIe for the rocket power, and the proper corrections in the elevator angle so that the vehicle will land at the chosen destination in spite of such disturbances. A schellIe of tracking and autollIatic navigation involving a high-speed cOllIputer and elevator servo is suggested for this purpose.T HE behavior of a vehicle flying thr'ough air is closely dependent upon the aerodynamic forces acting upon the vehicle. If, during one period of oscillation of the vehicle, there is appreciable variation of the response of aerodynamic forces to the attitude of the vehicle through variations in speed, in aerodynamic coefficients, in air density, etc., then the behavior of the disturbed flight path cannot be described by a linear differential equation of constant coefficients. In fact, the basic differential equation actually has coefficients that are specified functions of time. A very simple example of such motion is that of an artillery rocket during burning of the propellant grain. As shown by J. B. Rosser, R. R. Newton, and G. L. Gross (1),3 the basic differential equation for this particular case can be written as Bessel's differential equation for the order 1/2. The general character of the solutions of such differential equations is quite different from the character of solutions of differential equations with constant coefficients. For instance, while for equations with constant coefficients the stability of solutions for the homogeneous equation is generally sufficient to insure the stability of solutions with reasonable forcing functions, this simple state of affairs no longer prevails for equations with variable coefficients. The present theory of control and stability is built almost exclusively upon the theory of differential equations with constant coefficients. Therefore to study the disturbed motion of rockets, new methods have to be used.R. Drenick in a recent paper (2) demonstrated the usefulness of ballistic disturbance theory in solving the control and guidance problem of ballistic trajec-
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