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The vector field of the PMSM is analogous to the force field including four types of torque \u2014 inertial, internal, dissipative, and generalized external. Using the feedback thought, the error torque between external torque and dissipative torque is identified. The pitchfork bifurcation of the PMSM is performed. Four forms of energy are identified for the system \u2014 kinetic, potential, dissipative, and supplied. The physical interpretations of the decomposition of force and energy exchange are given. Casimir energy is stored energy, and its rate of change is the error power between the dissipative energy and the energy supplied to the motor. Error torque and error power influence the different types of dynamic modes. The Hamiltonian energy and Casimir energy are compared to find the function of each in producing the dynamic modes. A supremum bound for the chaotic attractor is proposed using the error power and Lagrange multiplier. <\/jats:p>","DOI":"10.1142\/s0218127417502169","type":"journal-article","created":{"date-parts":[[2018,1,28]],"date-time":"2018-01-28T22:58:05Z","timestamp":1517180285000},"page":"1750216","source":"Crossref","is-referenced-by-count":21,"title":["Force Analysis and Energy Operation of Chaotic System of Permanent-Magnet Synchronous Motor"],"prefix":"10.1142","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0059-4879","authenticated-orcid":false,"given":"Guoyuan","family":"Qi","sequence":"first","affiliation":[{"name":"Tianjin Key Laboratory of Advanced Technology of Electrical, Engineering and Energy, Tianjin Polytechnic University, Tianjin 300387, P. R. 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