Hamilton's modified principle applied to nonlinear circuit problems

Hamilton's Modified Principle (HMP) is used to solve two nonlinear problems. The amplitude, frequency, and stability in the limit cycle of a simple pentode oscillator are calculated in order to demonstrate the principle. A standard graphical method finds the amplitude of oscillations, and results are compared with experimental data. For the case under consideration, the HMP solution gives better agreement with the experimental results - 6.6% deviation as compared with 12.4% for the graphical solution. An approximate answer is also found for the transient behavior of a nonlinear system where the input is a step function. The result is compared with an analog computer solution and shows good agreement. The solution of a simple relay servo system is indicated in which the amplitude and frequency in the limit cycle along with its stability are obtained by application of the one method of HMP.