Динамика космической тросовой системы (The dynamics of space tether system)

Тип работы: 
Квалификационная работа магистра
Мунтян М. В.
Научный руководитель: 

Авраменко А. А.

Год защиты работы: 

В работе рассматривается задача моделирования космической тросовой системы, прикрепленной к поверхности Фобоса, спутника Марса, при малых отклонениях от устойчивой радиальной конфигурации. Целью работы является исследование малых колебаний тросовой системы, прикрепленной к поверхности спутника планеты, около устойчивого радиального положения.

Рассмотрены различные модели для исследования движения тросовой системы. Модель с невесомым тросом позволяет выявить ряд качественных особенностей движения тросовой системы и является простым средством оценки поведения тросовой системы на орбите и проверки любой более сложной модели в предельном случае.


Материалы защиты магистерской диссертации на английском языке, проведенной 16 июня 2010 года.

2. What is space tether system?

The space tether system is a complex of artificial space objects, connected by long, thin flexible elements which perform orbital flight. In its simplest form it is a bunch of two spacecraft connected by a rope with length of tens or even hundreds of kilometers. Space tether system is a new, innovative structure created by man in space. This system allows us to perform tasks that are impossible, impractical or uneconomical to solve by existing means of space technology.

Rope system can be used at transport, energy and research spheres, as well as for stabilization and control of spacecraft.

Now such systems are used on satellites to slow the rotation around the center of mass, for the insurance of astronauts when EVA (ExtraVehicular Activity), for communication of satellites and bring them into a state of gravitational stabilization.

5. Model with weightless tether

In history the model of weightless tether was the first model used to research movement of a rope system in orbit. It allows to ascertain the main features of the movement of tether system and it is the simple mean of evaluation.

These equations don’t describe true motion, if the rope is not pulled, therefore we should check $r>l$ ($r$ greater than $l$). In this research analyze the initial conditions for the integration of the system was performed under which the rope remains pulled.

6. A discrete model of a massive tether

The rope is divided into $n$ parts, that has a small length of the rods with joints at the ends. Consider the planar motion of a mechanical system. The mass of the tether is evenly distributed between the joints. The rods are weightless.

7. Model with a flexible inextensible tether

Consider the tether as a flexible heavy cord with enenly distributed mass. The position of point s on the cord located between points A and B at time t relative to the axes OXYZ is determined by aereocentric radius – vector $R(s,t)$. Equation of relation obtained from the condition of inextensible tether

8. Transverse oscillations of radial tether system

The eigenvalue problem for the transverse oscillations is given by

\frac{d}{d \xi} \left( (1-\xi)^2 \frac{d \Phi}{d \xi} \right) + \nu (\nu + 1) \Phi = 0, \ \left( \xi \frac{d \Phi}{d \xi} \right)_{AB} = \nu (\nu+1) \Phi_{AB}.
where $\xi$ - relative length, $\Phi$ - function that determines the form of transverse oscillations

General solution of this differential equation is expressed through the Lagrange functions of the first and second kinds

\Phi = c_1 P_\nu (\xi) + c_2 Q_\nu (\xi)

Using the boundary conditions, the frequency equation is obtained, solving which the sequence of roots $\nu_n$ is obtained.