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<p>Nonholonomic constrained systems are widely encountered in engineering and the natural sciences. Because the constraints are not integrable, analytical solutions are often difficult to obtain. This paper employs the Lie series method to derive analytical solutions for three classic examples: the Appel-Hamel system, the Chaplygin Sleigh system, and the Rosenberg system. The proposed Lie series solution was found to be consistent with the first integral of the corresponding system. Furthermore, numerical calculations verified consistency among the analytical solution, the first integral, and the numerical solution obtained with the ode45 function.</p>

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Lie series solution of nonholonomic constraint systems

  • 期刊论文

  • 发表日期：

    2026年7月18日

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  • Xinqian Li,
  • Yuhan Song,
  • Chang Liu

摘要

Nonholonomic constrained systems are widely encountered in engineering and the natural sciences. Because the constraints are not integrable, analytical solutions are often difficult to obtain. This paper employs the Lie series method to derive analytical solutions for three classic examples: the Appel-Hamel system, the Chaplygin Sleigh system, and the Rosenberg system. The proposed Lie series solution was found to be consistent with the first integral of the corresponding system. Furthermore, numerical calculations verified consistency among the analytical solution, the first integral, and the numerical solution obtained with the ode45 function.