Analysis of resonance external stability

for asymmetric spacecraft in atmosphere

V.V.Lyubimov

Samara Engineering Institute of the Railway Transport

Russia 443066, Samara, 1-st Bezymyannyj per., 18

e-mail: vlyibimov@mail.ru

In modern space research for delivery of a useful load on a earthly surface unguided space vehicles are widely used. Usually, the given vehicles are designed the symmetric form. However, at manufacturing and operation, as a rule, does not manage to achieve complete symmetry of a vehicle. Being present on space vehicle the small asymmetry can result in concurrence of frequencies of movement of a vehicle concerning a centre of mass and realization long resonance. In turn, the long resonance results in a significant increase of a angle of attack space vehicle, at which infringement of functional restrictions on a specified angle in a point of input of a parachute system occurs. Hence, the small asymmetry can is the reason of loss space vehicle and result in failure of the target program of flight.

The initial nonlinear system of equations of movement space vehicle concerning a centre of mass is difficult for research of the laws of change slow variable on nonresonant sites of movement, called by secondary resonant effects. Therefore for the decision of a given problem approximate nonlinear equations of movement space vehicle, received from a initial system are used. The given system of equations, in difference from initial two frequent, has a kind of a standard system with one fast phase and two slow variable: by a angle of attack and angular speed of rotation concerning a axis of symmetry. The reference in zero of resonant frequency in a equation for a fast phase corresponds to a main resonance in a initial system. External stability of a resonance is analyzed by a Lyapunov method with use of a differential equation for a finding of resonant frequency. With this purpose to a given equation a method of averaging on a fast phase on nonresonant sites of movement is applied.

In given work external stability of a main resonance is analyzed for the space vehicle with mass, aerodynamic and inertial asymmetry in atmosphere.