Energy cycle of brushless DC motor chaotic system

The vector field of the brushless DC motor (BLDCM) chaotic system is regarded as the force field of a pure mechanical system via the transformation of Kolmogorov system. The BLDCM force field is decomposed into four types of torque: inertial, internal, dissipative, and generalized external torque. The forcing effect of each term in the force field is identified via the analogue of the electrical and mechanical system. The BLDCM energy transformation of four forms of energy-kinetic, potential, dissipative, and generalized external is investigated. The physical interpretation of force decomposition and energy exchange is given. The rate of change of the Casimir energy is equivalent to the power exchanged between the dissipative energy and the energy supplied to the motor, and it governs the different dynamic modes. A simple and optimal supremum bound for the chaotic attractor is proposed using the Casimir function and optimization.