Acta Mechanica

, Volume 229, Issue 6, pp 2299–2306 | Cite as

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

Original Paper

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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Notes

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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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Naval Architecture and Ocean EngineeringJiangsu University of Science and TechnologyZhenjiangChina
  2. 2.College of Energy and Power EngineeringJiangsu University of Science and TechnologyZhenjiangChina
  3. 3.School of Applied ScienceBeijing Information Science and Technology UniversityBeijingChina

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