Monte Carlo simulations are an important tool in modern-day studies of many physical systems. Where unlikely events are to be simulated, the importance sampling technique can considerably ease the processing burdon, without compromising statistical significance. Here a comparison of importance sampling and standard Monte Carlo simulations is given. Emphasis is on variance reduction, and on the simulation gain of importance sampling, which is calculated explicitly for a simple example.

The physics of the fly-ball governor, introduced to regulate the speed of steam engines, is here analysed anew. The original analysis is generalized to arbitrary governor geometry. The well-known stability criterion for the linearized system breaks down for large excursions from equilibrium; we show approximately how this criterion changes.

The nonlinear dynamics of automobile braking are investigated. Nonlinearity arises because of the manner in which the friction coefficient between vehicle tyres and road surface depends upon vehicle speed and wheel angular speed. We show how antilock brake systems approach optimum braking performance.

Albatrosses have evolved to soar and glide efficiently. By maximizing their liftto-drag ratio L/D, albatrosses can gain energy from the wind and can travel long distances with little effort. We simplify the difficult aerodynamic equations of motion by assuming that albatrosses maintain a constant L/D. Analytic solutions to the simplified equations provide an instructive and appealing example of fixed-wing aerodynamics suitable for undergraduate demonstration.

We present a model of curling rock motion, which yields realistic dependence upon the dynamical parameters. The underlying assumptions are motivated by physical arguments. We make clear which of the model predictions depend upon the assumptions made about frictional asymmetry and which are independent of these assumptions. PACS Nos.: 45.20