Hamiltonian-Based Energy Analysis for Brushless DC Motor Chaotic System

The generalized Hamiltonian function is proposed for the brushless DC motor (BLDCM) chaotic system. The Hamiltonian and Casimir functions are derived from the generalized Hamiltonian function. In this way the Casimir energy is proven to be a special type of the generalized Hamiltonian function. The derivative of the Hamiltonian function is used for analyzing the various dynamical behaviors under different combination of energy components. An analytical optimal bound of the BLDCM is simply proposed from the Hamiltonian power. Along the study, the comparison between the Hamiltonian and Casimir powers is conducted, and physical interpretations and mechanism revealing the onset of chaos are provided for the BLDCM chaotic system. Bifurcation analysis through the Hamiltonian power and Casimir power identifies the different dynamic patterns.