What is an absolutely rough plane? Can you give an analytical expression of one? Why cannot a rigid body slide on a rough plane? Why does the point of contact not move in an infinitesimal movement of the body? Is there any website that treats the subject?
2026-03-26 02:51:17.1774493477
Absolutely rough planes
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I'm assuming absolutely rough means absolutely not smooth. Smoothness is like having local continuity and differentiability of the manifold, so an absolutely rough plane would be absolutely discontinuous in those regards I imagine. Another way of looking at this would be to require that the topological space it occupies is not anywhere locally homeomorphic to some otherwise-satisfactory Hausdorff space. The pathological expressions for such a plane are beyond me. I don't see how a rigid body comes into this. Such a manifold might have infinite friction I suppose what with all of the space that the surface will cover being discontinuous everywhere. The potential points of contact is such cases are not next to each other, hence you cannot move infinitesimally from one point to the next. All of this is just my intuition, so you can probably ignore me.