This paper is concerned with the analysis of the influence of the friction model on the existence of additional integrals of motion in a system describing the sliding of a spherical top on a plane. We consider a model in which the friction is described not only by the force applied at the point of contact, but also by an additional friction torque. It is shown that, depending on the chosen friction model, the system admits various first integrals. In particular, we give examples of friction models in which either the Jellett integral or the Lagrange integral or the area integral is preserved.

中文翻译：

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带有摩擦的平面上球面顶部的守恒定律

本文关注的是在描述球形顶部在平面上滑动的系统中，分析摩擦模型对运动附加积分存在的影响。我们考虑一个模型，其中不仅通过接触点施加的力来描述摩擦，而且还通过附加的摩擦力矩来描述。结果表明，根据所选的摩擦模型，系统允许使用各种第一积分。特别是，我们给出了保留Jellett积分或Lagrange积分或面积积分的摩擦模型的示例。