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Techniques for searching first integrals by lie group and application to gyroscope system

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Abstract

In the paper, the methods of finding first integrals of an autonomous system using one-parameter Lie groups are discussed. A class of nontrivial one-parameter Lie groups admitted by the classical gyroscope system is found, and based on the properties of first integral determined by the one-parameter Lie group, the fourth first integral of the gyroscope system in Euler case, Lagrange case and Kovalevskaya case can be obtained in a uniform idea. An error on the fourth first integral in general Kovalevskaya case (A = B = 2C,zG = 0), which appeared in literature is found and corrected.

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Authors and Affiliations

  1. Department of Mathematics, School of Science, Beijing Jiaotong University, 100044, Beijing, China

    Yanxia Hu & Keying Guan

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  1. Yanxia Hu
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  2. Keying Guan
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Correspondence to Yanxia Hu or Keying Guan.

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Hu, Y., Guan, K. Techniques for searching first integrals by lie group and application to gyroscope system. Sci. China Ser. A-Math. 48, 1135–1143 (2005). https://doi.org/10.1360/04ys0141

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