Algebraic structure and Poisson brackets of single degree of freedom non-material volumes
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This paper investigates an algebraic structure and Poisson theory of single degree of freedom non-material volumes. The equations of motion are proposed in a contravariant algebraic form, and an algebraic product is determined. A consistent algebraic structure and a Lie algebra structure are proposed, and a proposition is obtained. The Poisson theory of the non-material volume is established, and five theorems are derived. Three examples are given to illustrate the application of the method.
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This work was supported by the National Natural Science Foundation of China (Nos. 11702119, 51609110, 11502071), the Natural Science Foundation of Jiangsu Province (No. BK20170565) and the Innovation Foundation of Jiangsu University of Science and Technology (1012931609, 1014801501-6).
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