Generalized Rotation Tensor of An Arbitrary Spatial System of Forces
Gevorgyan H.A.
Gevorgyan H.A., Senior Researcher, Doctor of Philosophy in Engineering, Institute of Mechanics of the National Academy of Sciences of Armenia, Yerevan.
Manuscript received on 17 January 2024 | First Revised Manuscript received on 04 March 2025 | Second Revised Manuscript received on 06 June 2025 | Manuscript Accepted on 15 June 2025 | Manuscript published on 30 June 2025 | PP: 19-23 | Volume-12 Issue-6, June 2025 | Retrieval Number: 100.1/ijies.L100614011224 | DOI: 10.35940/ijies.L1006.12060625
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: The proposed article presents an extension of the wellknown theorem of theoretical mechanics about three moments, which is valid for an arbitrary planar 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.
Keywords: Second Form of Equilibrium, Arbitrary Spatial System of Forces, Moment Tensor, Generalised Rotation, Generalised Rotation Tensor.
Scope of the Article: Artificial Intelligence and Methods