Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2512.08302

Möbius Transformations and the Analytic--Geometric Reconstruction of the Induction--Machine Circle Diagram

Anubhav Gupta
View original source ↗Read source document ↗Export metadata ↓

Abstract

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.

Explore related subjects

math.DScs.SYeess.SYmath.CV

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Anubhav Gupta. 2025-12-09. Möbius Transformations and the Analytic--Geometric Reconstruction of the Induction--Machine Circle Diagram. https://arxiv.org/abs/2512.08302

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Effective equidistribution of orbits under semisimple groups on congruence quotients

We prove an effective equidistribution result for periodic orbits of semisimple groups on congruence quotients of an ambient semisimple group.This extends a previous work of Einsiedler, Margulis and Venkatesh. The main new feature is that we allow for periodic orbits of semisimple groups with nontrivial centralizer in the ambient group. Our proof uses crucially an effective closing lemma from work of the author with Lindenstrauss, Margulis,Mohammadi, and Shah.

math.DS↗
arXiv2026

Generalized entropy of measure-induced maps

A classical result by E. Glasner and B. Weiss states that the topological entropy of a map $f$ is zero if and only if the topological entropy of its measure-induced map $f_*$ is zero, where $f_*$ is defined as the push-forward of a measure. In this work, we use generalized entropy to distinguish the complexity of these maps and prove that the measure-induced map is much more complex than the original map. Moreover, we introduce the generalized mean dimension, an invariant that is useful for distinguishing dynamical systems with zero mean dimension, including those with the small-boundary property, and we show a relationship between this new invariant and generalized entropy.

math.DS↗
arXiv2026

The endpoint problem for $\varepsilon$-hypercyclicity

For a fixed $0<\varepsilon<1$, F. Bayart asked in 2024 whether there exists an operator $T$ such that, for every $0<δ<1$, $T$ is $δ$-hypercyclic if and only if $δ\in[\varepsilon,1)$. We answer this question affirmatively by constructing a weighted backward shift on $\ell_2(\mathbb N_0,\ell_2(\mathbb N_0))$ with this property.

math.DS↗