Ivanov

In this article, new equations called Condensed Lagrange equations (CLE) are defined. With their help, the rigid body absolute general motion is studied. The rigid body is considered to be homogeneous and unsymmetrical. CLEs are similar in structure to the classical Lagrange equations from second type, applied in vector-matrix form, but CLE are differing from them by four indicators. These differences are commented in detail in this article. The use of the CLE is fully equivalent to the application of the theorem, called Theorem for change of the rigid body generalized impulse. Using CLEs the differential equations in a matrix form, describing the rigid body absolute general motion, are obtained. CLEs enrich the theory of Rigid Body Mechanics. Moreover, CLEs represent a second alternative variant of the Theorem for change of the rigid body generalized impulse, they serve for verification, and finally, they make the study completely.

Submitted: 26/10/2019

Accepted: 29/10/2019

Published: 22/11/2019

*Corresponding Author

Anastas Ivanov

E-mail: aii2010@abv.bg

Keywords:

rigid body mechanics; condensed Lagrange equations; absolute general motion

Return to Content View [Full Article - PDF]

[Full Article - HTML] [Full Article - EPUB]

Post-Publication Peer-review Rundown

View/get involved, click [Peer-review]

REFERENCES

Awrejcewicz J., Koruba Z., (2012). Classical Mechanics.Applied Mechanics and Mechatronics, Springer.

CayleyA. (1858). A memoir on the theory of matrices. Philosophical Transactions of the Royal Society of

London, vol. 148, 17-37.

Dolapchiev B.I., (1969). Summary of the Nilsen-Tzenov equations.Bulletin of the BulgarianAcademy of Sciences.Mathematics, № 10.

Eiserman M.A., (1974). Classical Mechanics. Moscow, Nauka. (in Russian)

Featherstone R., (2008). Rigid Body Dynamics. Algorithms. Springer Science and Business Media, LLC.

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

Ivanov A.I., (2017), Theoretical Matrix Study of Rigid Body Pseudo Translational Motion. Greener Journal of Physics and Natural Sciences, 3 (2), 021-031.

Ivanov A.I., (2018). Motion of Asymmetrical Rigid Body in Fluid Area. Annual of the University of Architecture, Civil Engineering and Geodesy, 51 (2), 93-115. (in Bulgarian).

Ivanov A.I., (2018). Motion of Ellipsoid in Fluid Area. Annual of the University of Architecture, Civil Engineering and Geodesy, 51 (2), 117-136. (in Bulgarian).

Pars L.A., (1964). A Treatise on Analytical Dynamics. London, Heineman.

Suslov G.K., (1976). Fundamentals of Analytical Mechanics. Sofia, Nauka. (in Bulgarian)

Tzenov I.A., (1953). On a new form of equations of Analytical Mechanics.Moscow, DAN, USSR, vol. 89, book 1. (in Russian)

Wittenburg J., (1977). Dynamics of Multibody Systems.Springer-Verlag.

Zlatev I.S., (1965). Theoretical Mechanics.Sofia, Nauka i Izkustvo. (in Bulgarian)

Cite this Article: Ivanov A (2019). Condensed Lagrange Equations in Theoretical Mechanics. Greener Journal of Physics and Natural Sciences, 4(1): 1-6, https://doi.org/10.15580/GJPNS.2019.1.102619193.

Call for Papers

Call for Scholarly Articles

Authors from around the world are invited to send scholary articles that suits the scope of this journal. The journal is currently open to submissions and will process articles promptly and publish ready articles daily in each current issue.

The journal is centered on quality and goes about its processes in a very timely fashion. Seasoned editors/reviewers will be consulted to review each article(s), profer quality evaluations and polish the articles with expertise before publication.

Simply send your article(s) as an e-mail attachment to manuscripts.igj@acad.gjournals.org or manuscripts.igj@gmail.com.

Greener Journal of Physics and Natural Sciences

Excellence and Timeliness

Choose Language

For Authors

Editorial Info.

Newsletter

Ivanov

Call for Papers

Search

Login Form

Other Journals

Sponsored