Möbius Transformations and the Analytic--Geometric Reconstruction of the Induction--Machine Circle Diagram
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914189486850048 |
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| author | Gupta, Anubhav |
| author_facet | Gupta, Anubhav |
| contents | The Heyland circle diagram is a classical graphical method for representing the steady--state behavior of induction machines using no--load and blocked--rotor test data. Despite its long pedagogical history, the traditional geometric construction has not been formalized within a closed analytic framework. This note develops a complete Euclidean reconstruction of the diagram using only the two measured phasors and elementary geometric operations, yielding a unique circle, a torque chord, a slip scale, and a maximum--torque point. We prove that this constructed circle coincides precisely with the analytic steady--state current locus obtained from the per--phase equivalent circuit. A Möbius transformation interpretation reveals the complex--analytic origin of the diagram's circularity and offers a compact explanation of its geometric structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08302 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Möbius Transformations and the Analytic--Geometric Reconstruction of the Induction--Machine Circle Diagram Gupta, Anubhav Dynamical Systems Systems and Control Complex Variables The Heyland circle diagram is a classical graphical method for representing the steady--state behavior of induction machines using no--load and blocked--rotor test data. Despite its long pedagogical history, the traditional geometric construction has not been formalized within a closed analytic framework. This note develops a complete Euclidean reconstruction of the diagram using only the two measured phasors and elementary geometric operations, yielding a unique circle, a torque chord, a slip scale, and a maximum--torque point. We prove that this constructed circle coincides precisely with the analytic steady--state current locus obtained from the per--phase equivalent circuit. A Möbius transformation interpretation reveals the complex--analytic origin of the diagram's circularity and offers a compact explanation of its geometric structure. |
| title | Möbius Transformations and the Analytic--Geometric Reconstruction of the Induction--Machine Circle Diagram |
| topic | Dynamical Systems Systems and Control Complex Variables |
| url | https://arxiv.org/abs/2512.08302 |