Applied Mathematics Seminar

In this talk, I will discuss the pendulum and the ideal heat engine as examples of dynamical systems. In the case of the pendulum, this approach leads to new, accurate solutions for the motion of both the simple and spherical pendulum, which reveal a lot of new physics. The high level of abstraction involved in the ideal heat engine, a crucial ingredient in understanding the second law of thermodynamics, makes understanding of this subject difficult. A thermomechanical model of an isothermal system can be formulated as a 3-dimensional dynamical system, which shows damped oscillatory approach to equilibrium, and can be used to test some ideas of Feynman on visualising such processes.