This chapter introduces action-angle variables and solves the general one dimensional conservative system. Bohr-Sommefeld quantization is shown to be the quantum analogue. Action angle variables for the radial Kepler problem are found to be generalized to the relativistic version. Action angle variables of the general integrable system are defined. The heavy top of Lagrange is solved as an example. The chapter includes an exercise to work out Kovalevskaya's surprising discovery of another solvable heavy top.
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