Moment of light pressure in the medium with resistance

Abstract

The paper describes the simulation of fast rotational motion of a dynamically asymmetric satellite relative to the centre of mass under the influence of the joint effect of the moment of forces of light pressure and resistance. It is assumed that the surface of the spacecraft is a surface of revolution. The medium creates a weak resistance proportional to the angular velocity of the rigid body's own rotation relative to the centre of mass. Orbital motions with an arbitrary eccentricity are considered given. The mathematical model of satellite motion in this formulation is described by a rigid system of differential equations: the fast variables are Euler angles, and the slow variables are the modulus of the angular momentum vector, the kinetic energy, and the angles of orientation of the angular momentum vector in space. Averaging is performed over the Euler-Poinsot motion. The averaged system of equations of body motion allows numerical simulation of the satellite's motion relative to the centre of mass. The study is carried out in a dimensionless form for a multiparameter system of equations. For numerical calculation, an implicit third-order Adams method is used to integrate systems of differential equations. A personal computational package was developed for the constructed mathematical model of the satellite, as well as a library for calculating the complete elliptic integrals of the first and second kinds. Numerical calculation allows one to obtain the functions of modulating the modulus of the satellite kinetic moment vector, its orientation angles to the orbit, as well as the satellite kinetic energy values. The analysis of the influence of the parameters of the problem on the nature of the motion of the satellite relative to the centre of mass is carried out. A qualitative picture was obtained of the influence of the initial values ​​of the angles of orientation of the kinetic moment vector, the geometry of the masses, the eccentricity of the orbit, the characteristic numbers of disturbing moments on the hodograph character of the kinetic moment vector. The hodograph of the kinetic moment vector in three-dimensional space is simulated for various values of the system parameters. To construct three-dimensional objects on the scene, according to the carried out numerical calculations, we developed our own software using DirectX technology in C# language, simulating a virtual laboratory of a numerical experiment.