The main point of this paper is an observation that behind the standard averaging procedure there lies some simple previously unobserved geometry. In particular, the averaged forces in a rapidly forced system are, as it turns out, the constraint forces of an associated auxiliary non-holonomic system. The curvature of these constraints enters the expression for the averaged system. For example, the curvature of the pursuit curve enters the averaged equation of the pendulum with vibrating suspension point. This observation gives a new physical and geometrical insight into the mechanics of the Paul traps and the stability of forced inverted pendula.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics