Geometry and physics of averaging with applications (Q1809396)

The paper contains a new observation on the well-studied problem of Hamiltonian systems with rapid time-dependence. The author notes that behind the standard averaging procedure there lies some simple geometry. In particular, the averaged forces in a rapidly forced system are the constraint forces of an associated auxiliary nonholonomic system and the curvature of these constraints enter the expression for the averaged system. This paper gives a new insight into the method of confinement of charged particles such as the Paul trap. A very simple physical explanation of stability of the inverted pendulum with vertically vibrating suspension is presented.