Research ArticleOpen AccessGoogle Scholar indexed
Torque Free Axi-Symmetric Gyros with Changing Moments of Inertia
Department of Mechanics, Collage of Engineering and Islamic Architecture, Umm Al-Qura University, Makkah, Saudi Arabia
Faculty of Science, Umm Al-Qura University, Makkah, Saudi Arabia
Math. Dept., Faculty of Science, Tanta University, Tanta, Egypt
- 1 Department of Mechanics, Collage of Engineering and Islamic Architecture, Umm Al-Qura University, Makkah, Saudi Arabia
- 2 Faculty of Science, Umm Al-Qura University, Makkah, Saudi Arabia
- 3 Math. Dept., Faculty of Science, Tanta University, Tanta, Egypt
Applied Mathematics·Volume 07 (2016)·Pages 1934–1942·Published 14 October 2016·DOI10.4236/am.2016.716159
Copy link · social · email
Abstract
The properties and characteristics of torque free gyros with rotational symmetry and changing moments of inertia are the subject of the subsequent discussion. It shall be understood that the symmetry can be expressed by the notation (A=B) which does not presuppose geometric symmetry, where A and B are the principle moments of inertia about x and y axes respectively. We study the case of a torque free gyro upon which no external torque is acting. The equations of motion are derived when the origin of the xyz-coordinate system coincides with the gyro’s mass center c. This study is useful for the satellites, which have rotational symmetry and changed inertia moments, the antennas and the solar power collector systems.
KeywordsThe Gyroscopic MotionsMoments of InertiaSatellitesAntennasSolar Power Collector Systems
- Goldstein, H. (1980) Classical Mechanics. 2nd Edition, Addison-Wesley, Reading.
- Goldstein, H., Poole, Ch.P. and Safko, J.L. (2002) Classical Mechanics. 3rd Edition, Addison-Wesley, Reading.
- Kittel, Ch., Knight, W.D. and Ruderman, M.A. (1965-1971) Mechanics. Berkeley Physics Course. McGraw-Hill, New York.
- Landau, L.D. and Lifschitz, E.M. (1976) Mechanics. Pergamon, New York.
- Butikov, E. (2006) Inertial Rotation of a Rigid Body. European Journal of Physics, 27, 913-922.
- Butikov, E. (2006) Free Rotation of an Axially Symmetrical Body. http://www.ifmo.ru/butikov/Applets/Precession.html
- Bruno, A.D. (2007) Analysis of the Euler-Poisson Equations by Methods of Power Geometry and Normal Form. Journal of Applied Mathematics and Mechanics, 71, 168-199. http://dx.doi.org/10.1016/j.jappmathmech.2007.06.002
- Amer, T.S. (2004) Motion of a Rigid Body Analogous to the Case of Euler and Poinsot. Analysis, 24, 305-315. http://dx.doi.org/10.1524/anly.2004.24.14.305
- Udwadia, F.E. and Kalaba, R.E. (2007) Analytical Dynamics: A New Approach.
- Eshagh, M. and Najafi Alamdari, M. (2007) Perturbations in Orbital Elements of a Low Earth Orbiting Satellite. Journal of the Earth & Space Physics, 33, 1-12.
- Kraus, J.D. and Marhefka, R.J. (2002) Antennas for all Applications. McGraw-Hill, New York.
- Balanis, C. (1997) Antenna Theory. John Wiley & Sons, New Jersey, Published simultaneously in Canada, 450-458.
- Price, H., Lupfert, E., Kearney, D., Zarza, E., Cohen, G., Gee, R. and Mahoney, R. (2002) Advances in Parabolic Trough Solar Power Technology. Journal of Solar Energy Engineering, 124, 109-125.