IJPAM: Volume 63, No. 1 (2010)

CONDITION OF FREE AND CONSTRAINED MOTION OF
CABLE CONNECTED SATELLITES SYSTEM
IN LOW ALTITUDE ORBIT

A. Narayan$^1$, M.D. Pandey$^2$
$^{1,2}$Department of Mathematics
Bhilai Institute of Technology
Bhilai House, Durg, Chhattisgarh, 491001, INDIA
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]


Abstract.Combined effects of the Earth's magnetic field and oblateness of the Earth on the stability of two satellites connected by a light, flexible and inextensible cable in the central gravitational field of the Earth have been studied. The equations of motion of the system have been deduced with respect to the centre of mass, which assumed to move along a low altitude equatorial orbit. We have considered the dipole of the Earth has its axis inclined from the polar axis of the Earth by $11^{0}24'$. We have transformed the equation of motion in polar-spherical co-ordinate system to analyze the problem. The Jacobi integral exists for the problem and hence with the help of this integral we have analyzed the condition of free and constrained motion. We have adopted simulation technique using MATLAB 6.1 to analyse the free and constrained motion of the cable connected system moving in a low altitude equatorial orbit.

Received: July 5, 2010

AMS Subject Classification: 70F15

Key Words and Phrases: cable connected satellites, magnetic field of the Earth, oblateness of the Earth, free and constrained motion

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 63
Issue: 1