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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