# IJPAM: Volume 63, No. 1 (2010)

**CONDITION OF FREE AND CONSTRAINED MOTION OF**

CABLE CONNECTED SATELLITES SYSTEM

IN LOW ALTITUDE ORBIT

CABLE CONNECTED SATELLITES SYSTEM

IN LOW ALTITUDE ORBIT

Department of Mathematics

Bhilai Institute of Technology

Bhilai House, Durg, Chhattisgarh, 491001, INDIA

e-mail: ashu_1959@rediffmail.com

e-mail: mithileshpandey_1978@yahoo.co.in

**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 . 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