In this talk I shall I shall present some recent work on a favorite topic--- averaging theory for controlled mechanical systems with oscillatory inputs. Some particular points on which I hope to touch are:

1. The geometric distinction between veolicity controlled and acceleration controlled mechanical systems,
2. Geometric conditions for stable response to oscillatory forcing,
3. Interesting physical examples, and, time permitting,
4. Scale-invariance of the effects of oscillatory control.

I have chosen to emphasize these points because I believe they can be related in various ways to work of colleagues attending the workshop.

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