Generalized Rotation Tensor of An Arbitrary Spatial System of Forces
Article Sidebar
Main Article Content
Abstract
The proposed article presents an extension of the wellknown theorem of theoretical mechanics about three moments, which is valid for an arbitrary plate system of forces, to the general case of an arbitrary spatial system of forces. Existence and uniqueness theorems for a symmetric static tensor of moments are formulated with a presentation of their proofs. For an arbitrary spatial system of forces, the dynamic tensor of moments is also formulated. A technique is presented for determining the principal directions and principal values of the moment tensor, for which the number of its independent components is reduced to three. This case provides clear evidence for the existence of a generalized rotation. A concrete example of an arbitrary system of forces is given, confirming the equivalence of the conditions of static equilibrium in the classical and new interpretations.
Downloads
Article Details
Section
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
How to Cite
References
Butenin N.V., Lunts Ya.L., Merkin D.R. Course of Theoretical Mechanics: Statics and Kinematics (volume 1). – M.: Science. Fizmatlit, 1979. – 272 p. http://dx.doi.org/10.36994/978-966-388-611-4-2021-142
Loitsyansky L.G., Lurie A.I. Course of Theoretical Mechanics: Statics and Kinematics (volume 1). 8th ed., revised. And additional – M.: Nauka, 1982. – 352 p. https://www.livre-rare-book.com/book/30016025/alb4c417645257a6e77
Buchholz N.N. Basic course of theoretical mechanics. At 2 h. Part 1. Kinematics, statics, and dynamics of a material point. – M.: Nauka, 1972. – 467 p.
https://www.scirp.org/reference/referencespapers?referenceid=1818724
Nikolai E.L. Theoretical mechanics. In 2 vols. T. 1. Statics. Kinematics. – M .: State. ed.-in f.-m. Literature, 20th edition, 1962. – 280 p. https://www.amazon.in/Theoretical-Mechanics-Nikolai-G-Chetaev/dp/3540513795
Yablonsky A.A., Nikiforova V.M. Course of theoretical mechanics. At 2 h. Part 1. Statics and kinematics. – M .: Higher School, 3rd edition, 1966. – 432 p.
Butenin N.V., Lunts Ya.L., Merkin D.R. Course of theoretical mechanics. – St. Petersburg: Lan, 2009. – 736 p.
https://engjournal.bmstu.ru/articles/1347/eng/1347.pdf
Kilchevsky N.A. Elements of tensor analysis and its application to mechanics. – M.: Nauka, 1954. https://scispace.com/pdf/tensor-analysis-with-applications-in-mechanics-lvdsbpdker.pdf
Velichenko V.V. Geometrical mechanics: foundations of the theory and fundamental equations // PMM. 2014. T. 78.