AI 中文总结
重新审视F. Génot和B. Brogliato对经典Painlevé问题的分析，发现其关于机械系统动力学演化的结论不具伽利略观察者不变性，运动状态分类依赖观察者，源于伽利略速度相加定理，还探讨了恢复观察者不变描述的模型 reformulations。
AI 中文摘要
我们重新审视了F. Génot和B. Brogliato对经典Painlevé问题的分析（[1]《Painlevé悖论的新结果》-《欧洲固体力学杂志-A辑》，18(4):653 - 677，1999），重点关注其结果与伽利略不变性的一致性。我们表明，关于机械系统动力学演化的某些结论在伽利略观察者变化下并非不变，因此以其当前形式不能被解释为系统的固有属性。特别是，我们表明运动状态的分类取决于观察者，这通过摩擦约束的速度相关特征体现，我们将这种依赖性追溯到伽利略速度相加定理。我们提出并讨论了旨在恢复问题的观察者不变描述的模型可能的重新表述。
英文摘要
We reconsider the analysis of the Classical Painlevé Problem developed by F. Génot and B. Brogliato ([1] New results on Painlevé paradoxes. - European Journal of Mechanics-A/Solids, 18(4):653{677, 1999), focusing on the consistency of their results with Galilean invariance. We show that certain conclusions concerning the dynamical evolution of the mechanical system are not invariant under changes of Galilean observer and therefore cannot, in their present form, be interpreted as intrinsic properties of the system. In particular, we show that the classi?cation of motion states depends on the observer through the velocity{dependent characterization of the frictional constraint, and we trace the origin of this dependence to the Galilean velocity-addition theorem. We present and discuss possible reformulations of the model aimed at restoring observer-invariant descriptions of the problem.
Comments16 pages, 4 figures
