Greener Journal of Physics and Natural Sciences

Open Access


Greener Journal of Physics and Natural Sciences Vol. 3 (2), pp. 021-031, October 2017.

  © 2017 Greener Journals

Research Paper

Manuscript Number: 101117147



Theoretical Matrix Study of Rigid Body Pseudo Translational Motion


Anastas Ivanov


Todor Kableshkov University of Transport, Sofia, Bulgaria.


In this paper, a pseudo translational motion of free asymmetrical rigid body to an absolute reference system is studied. A private kind of Theorem of change of generalized body impulse is formulated. This theorem is called Theorem of change of pseudo generalized body impulse. A private kind of Condensed Lagrange equations is formulated. These equations are called Condensed Lagrange equations for study of pseudo translational motion of free asymmetrical rigid body. Using that theorem and those equations, the pseudo translational motion of the rigid body is successfully studied. The paper is theoretical, but it gives a base for a number of applications. For example, these are investigations of the motion, stability and management of satellite. The other main application is free or forced small body vibrations. Moreover, the obtained formulas are appropriate for computer numerical integrations by contemporary mathematical programs.


Key words: rigid body, pseudo translational motion, generalized body impulse, condensed Lagrange equations.

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Ivanov A. I., Theoretical Matrix Study of Rigid Body General Motion. Greener Journal of Physics and Natural Sciences, vol. 3 (2), pp. 009-020 (2017).


Ivanov A. I., Kinamatics of Pseudo Translational Motion of Rigid Body. Ac. J. Mechanics, Transport, Communications, vol. 15 (1), pp. 7-15, (2017).


Яблонский А. А., Норейко С. С., Курс теории колебаний. Лань, Санкт-Петербург, Москва, Краснодар (2003), 248.


Tse F. S., Morse I. E., Hinkle R. T., Mechanical Vibrations. Allyn and Bacon, Inc., Boston (1963), 508.


Rao, S. S., Mechanical Vibrations. Prentice Hall, Boston (2004, 2011), 1084.


Palm, W. J., MatLab for Engineering Applications. McGraw-Hill, (1998).


Rao, V. D., MatLab. An Introduction and Applications. New Age International (P) Lt., Publishers, (2010), 665.


Bathe, K. J. Finite Element Procedures. Prentice Hall, Pearson Education, Inc. (2016), 1043.


Moaveni, S., Finite Element Analysis, Theory and Application with ANSYS. Prentice Hall, Inc., New Jersey (1999), 527.


Logan, L. D. A First Course in Finite Element Method. Nelson, a division of Thomson Canada Limited., (2007), 836


Goldstein H., Poole C., Safko J., Classical Mechanics. Columbia Univ., Univ. of South Carolina, (2000), 1-646.

Baez J. C., Derek K. W., Lectures on Classical Mechanics. (2005), 77.


Tong D., Classical Dynamics. Wilberforce Road, UK (2005), 139.


Arovas D., Lectures Notes on Classical Mechanics. Department of Physics, Univ. of California, San Diego (2013), 453.