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Algebraic structure and Poisson brackets of single degree of freedom non-material volumes

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Abstract

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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Acknowledgements

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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Authors and Affiliations

  1. School of Naval Architecture and Ocean Engineering, Jiangsu University of Science and Technology, Zhenjiang, 212003, China

    Wen-An Jiang & Kun Liu

  2. College of Energy and Power Engineering, Jiangsu University of Science and Technology, Zhenjiang, 212003, China

    Zhao-Wang Xia

  3. School of Applied Science, Beijing Information Science and Technology University, Beijing, 100192, China

    Li-Li Xia

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  1. Wen-An Jiang
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  2. Kun Liu
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  3. Zhao-Wang Xia
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  4. Li-Li Xia
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Correspondence to Wen-An Jiang.

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Jiang, WA., Liu, K., Xia, ZW. et al. Algebraic structure and Poisson brackets of single degree of freedom non-material volumes. Acta Mech 229, 2299–2306 (2018). https://doi.org/10.1007/s00707-018-2119-1

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  • DOI: https://doi.org/10.1007/s00707-018-2119-1

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