Teaching Physics (and more) with Niven


Because a system can be stable with respect to disturbances in one direction, but not in another, it’s useful to show the potential energy as a surface, not a curve. This chart shows the classic “saddle-shaped” equilibrium, stable in one direction but not another, just like the Ringworld. In addition to the Ring, this chart describes inertial navigation systems – a slight initial horizontal velocity error will cause 84-minute oscillations, requiring slight damping to control, while a slight vertical velocity error will grow without limit unless heavily damped. 84-minutes, by the way, is the natural period of an earth-radius pendulum, the natural period of horizontal velocity errors in an inertial navigation system, the period of a ground level Earth satellite, and the period of motion for an object in a tunnel from New York to London, New York to Beijing or New York to Chicago – it’s also a dessert topping and a floor wax.

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