On a Disk Sliding on a Rough Inclined Plane under an Arbitrary Law of Normal Stresses

摘要

The paper deals with the problem of a disk sliding on a rough inclined plane under the action of an arbitrary (symmetric) law of normal stress distribution and the classical differential Euler–Coulomb dry friction law. Some qualitative results concerned with the global dynamics of motion of such a disk are obtained. In several cases where the Galin distribution of normal stresses and the corresponding Zhuravlev formulas for friction forces andmoments are used, one can succeed in obtaining the first integrals for the corresponding equations of motion of an annular disk. The limit cases concerned with the well-posedness of transition from a disk to a material point, which is directly related to the problem of justification of the point contact with sliding friction or a nonholonomic constraint, are also discussed.