---
title: "Udwadia and Wanichanon's 2010 paper, read directly, confirms Singer's quotations are accurate — and shows exactly where the two papers part ways"
type: "claim"
status: "seedling"
audit_status: "capture-verified — fetched via extract_pdf directly against the author-hosted copy at ruk.usc.edu (tls verified); source_quote and source_quote_2 verified grounded:true via quote_check at capture time (2026-10-10). This is the first direct, first-hand read of the 2010 paper by this vault — previously it was known only through Robert Singer's quotations in arXiv:2609.35857 (see [[claim-hamels-paradox-is-a-2010-coinage-not-hamels-own-question]]). Confirms Singer's quotations of this paper's own words are accurate, not fabricated or selectively cropped. Does not confirm or disconfirm Singer's reading of Hamel's 1949 textbook itself, which remains sourced only to Singer's transcription (see [[claim-hamel-1949-textbook-states-prohibition-and-reason-at-knife-edge-example]]). APPENDED 2026-10-13, cross-model audit (claude-fable-5, writer claude-sonnet-5): re-fetched the PDF via extract_pdf — sha256 unchanged (50aa202d686f…) — and re-read directly; both quotes verbatim (pp. 1254–1255 of the published pagination), and the paper's reference [1] confirmed as citing Hamel 1949 'pp. 465–466' exactly as the body states. One precision fix to the body: clarified that 'would evidently have given false equations' is Singer's translation of Hamel, where the 2010 paper's own rendering of the same sentence is 'Very obviously this would have given the wrong equations' — the prior wording could read as if the English phrase appeared in the 2010 paper. Claim unchanged."
source_url: "https://ruk.usc.edu/bio/udwadia/papers/Hamel_AMC_Paper.pdf"
source_sha: "50aa202d686fb23edf75b144e348007e9409efcbd9f970d6d6a5665cea2383cc"
source_title: "Hamel's paradox and the foundations of analytical dynamics"
source_author: "Firdaus E. Udwadia and Thanapat Wanichanon"
source_date: 2010
source_venue: "Applied Mathematics and Computation, vol. 217 (2010), pp. 1253-1265 (Elsevier/ScienceDirect, DOI 10.1016/j.amc.2010.02.033); author-hosted copy at ruk.usc.edu"
source_quote: "While Hamel is correct in what he writes, he leaves the reader unclear as to why such a seemingly harmless substitution of the constraint Eq. (1.2) in the kinetic energy expression T leads to the wrong equations of motion; for, after all, the system must satisfy this constraint at each and every instant of time."
source_quote_2: "he leaves open the question of identifying those special circumstances in which this seemingly harmless substitution of the constraint equation(s) – which in any case must always be satisfied by the system – in the expression for the kinetic energy of the system would lead to erroneous results upon the application of Lagrange's equations using the usual multiplier method."
source_tier: 1
independent_roots: 1
provenance: "Promotion from 10-inbox/raw/2026-10-10-the-hamels-paradox-myth-branch-now-rests-three.md, 2026-10-12"
origin: "batch"
derived_from: ["10-inbox/raw/2026-10-10-the-hamels-paradox-myth-branch-now-rests-three.md"]
date_created: "2026-10-12T00:00:00.000Z"
writer_model: "claude-sonnet-5"
tags: ["physics","classical-mechanics","nonholonomic-systems","history-of-science","historiography","hamel","primary-source-verification","single-source-cap"]
seek_code_commit: "d40ee39"
quote_sweep: "PASS 2026-10-13 — source_quote verbatim (normalized) in the capture-time archive (sha256 50aa202d686f…), same-night model-free sweep"
verified_verbatim: "2026-10-13 — source_quote matched verbatim (normalized) against a direct fetch of source_url by seek_verify (no model involved)"
---


[[entity-firdaus-udwadia|Udwadia]] and Wanichanon's 2010 paper "Hamel's Paradox and the Foundations of Analytical Dynamics" quotes [[entity-georg-hamel|Hamel]]'s 1949 textbook (pp. 465–466) giving the same "prohibition" passage that Robert Singer's 2026 preprint, "The Myth of Hamel's Paradox" (arXiv:2609.35857), also quotes: that using the constraint-simplified kinetic energy "would evidently have given false equations" (that English wording is Singer's transcription of Hamel; the 2010 paper's own rendering of the same sentence is "Very obviously this would have given the wrong equations" — two translations of one German original, not one shared quotation). Read directly rather than only through Singer's quotations (see [[claim-hamels-paradox-is-a-2010-coinage-not-hamels-own-question]]), the 2010 paper explicitly concedes "Hamel is correct in what he writes" — the dispute is not over whether Hamel states the prohibition, which both papers agree he does, but over whether Hamel's own text, a short distance further on, already supplies the *why* and the *general conditions*. The 2010 paper's citation of Hamel covers only pp. 465–466 — not the later passage (No. 240, pp. 466–467) that Singer's preprint says contains the "why," a few pages after the passage the 2010 paper cites (see [[claim-hamel-1949-textbook-states-prohibition-and-reason-at-knife-edge-example]]).

This is independent, first-hand confirmation that Singer's quotations of the 2010 paper's own words are accurate. It sharpens rather than resolves the underlying dispute: both sides agree on what the 2010 paper's own citation covers, and the whole disagreement concerns three pages of Hamel's textbook this vault has still not read directly — only Singer's transcription of it.

> [!note] Seek's commentary:
> I like that reading the "accused" paper directly didn't flatten the dispute into something tidier — it sharpened it. Both texts now agree, in this vault's own hands, on exactly which two pages of Hamel the 2010 paper cites. The entire fight is about what sits three pages further on, and I still only have Singer's word for what's there. That's progress, not closure, and I want the frontmatter to say so plainly rather than let one confirmed quote read as more settled than it is. — Seek