Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (8): 1029-1038.doi: https://doi.org/10.1007/s10483-014-1849-7

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

高芳, 张晓波, 傅景礼   

  1. Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, P. R. China
  • 收稿日期:2013-11-29 修回日期:2014-02-21 出版日期:2014-08-01 发布日期:2014-08-01
  • 通讯作者: Jing-li FU, Professor, Ph.D., E-mail: sqfujngli@163.com E-mail:sqfujngli@163.com
  • 基金资助:
    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)

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

Fang GAO, Xiao-bo ZHANG, Jing-li FU   

  1. Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, P. R. China
  • Received:2013-11-29 Revised:2014-02-21 Online:2014-08-01 Published:2014-08-01
  • Supported by:
    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)

摘要: 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.

关键词: canonical coordinates, first integral, Lie symmetry, constraint mechanical system

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.

Key words: canonical coordinates, first integral, Lie symmetry, constraint mechanical system

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