Вплив імпульсних рульових двигунів на динаміку твердопаливної ракети

The object of this study is a rocket with a solid propellant engine launched from a vehicle launcher. The current work studies the oscillations of a rocket airframe in flight under the influence of impulses of the steering motors and the effectiveness of flight control along the trajectory by the steering motors located in the head of the solid rocket. Analytical and numerical methods for determining the frequencies of free vibrations of a rigid body and analytical methods for integrating differential equations of motion are applied. A mathematical model of rocket flexural oscillations has been constructed. Methods for determining the modes and frequencies of natural oscillations have been analyzed. Three lower frequencies and modes of natural oscillations of the rocket were calculated. The discrepancy between the results of the calculation by the computer program and the analytical calculation of the first approximation is 3%. The calculation of oscillations of a rocket with a caliber of 30 mm and a length of 7655 mm showed that torsional and longitudinal oscillations have relatively high frequencies and have little effect on the stability and controllability of the rocket flight. The vibrations of the rocket airframe, which has a gas-dynamic flight control system with the help of rudders and a gas-jet one with the help of steering engines, are studied. Steering motors are small-sized disposable solid propellant motors, which are located in five rows around the perimeter of the rocket airframe at the head. Methods for calculating the forced oscillations of a rocket during the operation of steering engines have been developed. Under the action of the control pulse, transverse oscillations of the rocket airframe y are excited and simultaneously, the rocket rotates as a solid body around the center of mass. Airframe oscillations quickly decay, and rotation changes the pitch or slip angle. To stop the rotation and leave some required angle of inclination or azimuth of the trajectory, a second impulse of force must be given by the steering motor mounted on the opposite side of the hull. The dependence of the change in pitch and slip angles on the duration of time intervals between control pulses was studied. The analysis of the dependence obtained shows that, although the weight of the fuel charge is approximately half the weight of the rocket, the controllability by the steering engines is equally effective at any fuel consumption.