UBC Theses and Dissertations

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UBC Theses and Dissertations

The application of Lie derivatives in Lagrangian mechanics for the development of a general holonomic theory of electric machines Gustafson, Ture Kenneth


A general approach to the treatment of electrical machine systems is developed. Tensor concepts are adopted; however, metrical ideas are avoided in favour of Hamilton's Principle. Using Lie derivatives and choosing a holonomic reference system, the equations resulting are general, and thus apply to any physical system of machines. These equations are Faraday's Law for the electrical portion and a gradient equation for the mechanical portion. Transformation characteristics, which are found to be of two independent types, called the v-type and the i-type,are investigated. This leads to tensor character and invariance properties associated with the transformations. The equations of small oscillation, which are based on the general equations of motion obtained in the thesis, are derived for any physical system. In the final chapter two examples of application are given; the power selsyn system, and the synchronous machine.

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