Manipulation with vibratory velocity fields on a tilted plate

We examine the dynamics of point parts in frictional contact with a periodically vibrating, flat, rigid plate that is nominally tilted with respect to horizontal. If the friction law satisfies the maximum power inequality, then part dynamics on the tilted plate are equivalent to part dynamics on a horizontal plate with a different friction law that also satisfies the maximum power inequality. For small angles of tilt, this equivalence means that every periodic plate motion induces a position-dependent velocity field through which parts slide. Assuming Coulomb friction, some of the fields obtainable with a tilted plate are impossible to generate with a horizontal plate; other fields that require complicated motions on a horizontal plate can be generated with simpler motions on a tilted plate.