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Application of canonical coordinates for solving single-freedom constraint mechanical systems

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Abstract

This paper introduces the canonical coordinates method to obtain the first integral of a single-degree freedom constraint mechanical system that contains conservative and non-conservative constraint homonomic systems. The definition and properties of canonical coordinates are introduced. The relation between Lie point symmetries and the canonical coordinates of the constraint mechanical system are expressed. By this relation, the canonical coordinates can be obtained. Properties of the canonical coordinates and the Lie symmetry theory are used to seek the first integrals of constraint mechanical system. Three examples are used to show applications of the results.

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Authors and Affiliations

  1. Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou, 310018, P. R. China

    Fang Gao  (高 芳), Xiao-bo Zhang  (张晓波) & Jing-li Fu  (傅景礼)

Authors
  1. Fang Gao  (高 芳)
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  2. Xiao-bo Zhang  (张晓波)
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  3. Jing-li Fu  (傅景礼)
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Correspondence to Jing-li Fu  (傅景礼).

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11072218 and 11272287) and the Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT) (No. IRT13097)

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Gao, F., Zhang, Xb. & Fu, Jl. Application of canonical coordinates for solving single-freedom constraint mechanical systems. Appl. Math. Mech.-Engl. Ed. 35, 1029–1038 (2014). https://doi.org/10.1007/s10483-014-1849-7

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  • DOI: https://doi.org/10.1007/s10483-014-1849-7

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

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