On investigation of limit cycles behavior depending on the growth of aerodynamic parameter of orbital rope system motion in an elliptical orbit

Аuthors

Vorontsova V. L.

Institute of Management, Economics and Finance Kazan Federal University, KFU, 4, Butlerova str., Kazan, 420012, Russia

e-mail: VLVorontsova@yandex.ru

Abstract

The study of aerodynamics influence on the motion of an artificial cluster-satellite of two bodies is stipulated by the expansion of large extent orbital tether systems field of application. For such large space systems, aerodynamic effects are of a great significance. We have investigated the behavior of limit cycle for an equation of relative motion orbital cluster of two bodies considering impact of gravitational effect, aerodynamic pressure, airborne gradient and dissipative factors, depending on the growth of aerodynamic parameter a. We use the equations of interconnected motion with allowance for the forces of gravitational gradient and aerodynamic factors. We study the effect of aerodynamic parameters on the behavior of limit cycles. To carry out the research we implemented well-known methods of nonlinear mechanics: of Lagrange equations of the first kind method, phase plane method; points mapping method; theory of motion stability methods.

The main qualitative effect of the rotational motion of the satellite in an elliptical orbit is the possibility motion chaotization. The atmosphere creates especially strongly effects the beginning of chaotization due to the exponential change of its density in an elliptical orbit. Even relatively small eccentricities can enable strong chaotization.

For eccentricity values e = 0.001 and small values of the aerodynamic parameter a limit cycles are absent. The increase of aerodynamic parameter a leads to the emergence of limit cycles. For values of a fr om 4 to 45 there a limit cycle exists. The value of (( to which all points on the phase portrait roll down drops from 29.6 to 14.5. With a further increase of the parameter a (a > 45) lim it cycles disappear.

Keywords:

dynamics of space systems, qualitative theory of dynamical systems, orbital cluster of bodies, tether systems, limit cycles, phase space, aerodynamic parameter, orbit eccentricity

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