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There is now a CONTENT FREEZE for Mercury while we switch to a new platform. It began on Friday, March 10 at 6pm and will end on Wednesday, March 15 at noon. No new content can be created during this time, but all material in the system as of the beginning of the freeze will be migrated to the new platform, including users and groups. Functionally the new site is identical to the old one. webteam@gatech.edu
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Two classes of (interesting, at least to me) physical behavior follow from the impossibility of integrating some formulas that involve derivatives. First, systems with wheels or ice skates can be conservative yet have asymptotic stability. This is relevant to braking cars, flying arrows and the balance of skateboards and bicycles. Second, is the well known possibility that a system with zero angular momentum can, by appropriate deformations, rotate without any external torque. This effect explains how a cat that is dropped while upside down can turn over and of how various gymnastic maneuvers are performed. Both rolling contact and constancy of angular momentum are examples of the "non-integrability" of a "non-holonomic" equation. There are various simple demonstrations of these phenomena that can go bad. Cars can crash, bikes fall over and, in terrestrial experiments, various effects can swamp that which one wants to demonstrate. The talk describes the basic theory and then a collection of simple experiments that fail various ways for various reasons.
