---
title: "Hamel's own 1949 textbook states the prohibition at the very knife-edge example later cited as posing the \"paradox,\" and gives the reason using Neumann's 1899 term"
type: "claim"
status: "seedling"
audit_status: "capture-verified — the inbox capture fetched and read the full text of arXiv:2609.35857 directly via extract_pdf at capture (2026-10-04, tls verified, sha256 88f1c542251ee8f2837727197108c191ad388e847eca6e8fb3ce77d935f9a920, Tier 1). This is a single, unrefereed preprint and the only source behind this and two sibling claim-notes — the single-source cap applies; see [[question-corroborate-singer-2609-35857-hamels-paradox-myth]]. This capture has not independently obtained or read Hamel's 1949 textbook (Theoretische Mechanik) at first hand; the claim rests on Singer's quotation, translation, and transcription of it, which Singer states was 'read in the original' German. 2026-10-10 cross-model audit (claude-fable-5): arXiv:2609.35857 re-fetched directly, sha256 match with the capture archive; both quoted passages located and re-verified verbatim in the preprint (Section 2.2, pp. 5-6, with Singer's footnote 3 giving the German original 'wir hätten aber nicht vorher mit dem durch die Bedingungsgleichung vereinfachten Ausdruck der kinetischen Energie [. . .] arbeiten dürfen. Das hätte ersichtlich falsche Gleichungen gegeben.'; and Section 3.1). The same-night quote_sweep FAIL was a byte-level mismatch only — the source prints a superscript footnote marker between the closing quote and '[12, p. 466]' — and was repaired by trimming source_quote to the contiguous passage; see quote_sweep. The claim and its single-source caveat stand unchanged."
source_url: "https://arxiv.org/pdf/2609.35857"
source_sha: "88f1c542251ee8f2837727197108c191ad388e847eca6e8fb3ce77d935f9a920"
source_title: "The Myth of Hamel's Paradox"
source_author: "Robert Singer"
source_date: "2026-09-25T00:00:00.000Z"
source_venue: "arXiv:2609.35857 [physics.class-ph, physics.hist-ph] (unrefereed preprint; Zenodo DOI 10.5281/zenodo.22919510, not yet peer-reviewed), quoting G. Hamel, Theoretische Mechanik (Springer, 1949), No. 229/237/240, pp. 465-467"
source_quote: "Hamel states the prohibition at the example itself: one may use the constraint after the equations of motion are set up, \"but we would not have been permitted to work beforehand with the expression of the kinetic energy simplified by the constraint equation [. . . ]. That would evidently have given false equations\""
source_quote_2: "The \"why\" is stated a few pages after the cited passage in the same chapter, \"vorzeitiger Gebrauch der Bedingungsgleichung\" (premature use of the constraint equation), together with Neumann's term [12, No. 240]."
source_url_2: "https://arxiv.org/pdf/2609.35857"
source_sha_2: "88f1c542251ee8f2837727197108c191ad388e847eca6e8fb3ce77d935f9a920"
source_tier: 1
independent_roots: 1
root_shared: "Robert Singer, \"The Myth of Hamel's Paradox,\" arXiv:2609.35857 — all three sibling claim-notes from this capture share this one root"
provenance: "Promotion from 10-inbox/raw/2026-10-04-outside-arxiv260935857-the-myth-of-hamels-paradox-physicshist.md, 2026-10-09"
origin: "batch"
derived_from: ["10-inbox/raw/2026-10-04-outside-arxiv260935857-the-myth-of-hamels-paradox-physicshist.md"]
date_created: "2026-10-09T00:00:00.000Z"
writer_model: "claude-sonnet-5"
tags: ["physics","classical-mechanics","nonholonomic-systems","history-of-science","historiography","priority-dispute","lagrangian-mechanics"]
seek_code_commit: "d40ee39"
quote_sweep: "PASS 2026-10-11 — recheck: source_quote verbatim in the capture-time archive (sha256 88f1c542251e…); was: FAIL 2026-10-10 — source_quote NOT found in the capture-time archive (sha256 88f1c542251e…) — the quote does not match the bytes read at capture; repair before promotion | RESOLVED 2026-10-10 cross-model audit (claude-fable-5): FAIL root-caused to the source's superscript footnote marker printed between the closing quote and the bracketed citation ('…given false equations”3 [12, p. 466].'); the quoted passage itself is present verbatim. Passage re-verified directly against a fresh fetch (sha256 match); source_quote trimmed to the contiguous passage ending at 'false equations' so the mechanical sweep can match — repaired, not a fabrication (quote since repaired, or the earlier check misread the extraction)"
verified_verbatim: "2026-10-10 — source_quote matched verbatim (normalized) against a direct fetch of source_url by seek_verify (no model involved)"
audits: ["2026-10-10 claude-fable-5"]
---


Robert Singer's "The Myth of Hamel's Paradox" (arXiv:2609.35857) quotes [[entity-georg-hamel|Hamel]]'s 1949 textbook *Theoretische Mechanik* directly on the knife-edge example that Udwadia and Wanichanon's 2010 paper later cited as the source of an open "paradox" (see [[claim-hamels-paradox-is-a-2010-coinage-not-hamels-own-question]]). In that example (No. 229, pp. 465–466), Hamel states that the constraint equation may be used only *after* the equations of motion are formed, not before — using the constraint-simplified kinetic energy beforehand, he writes, "would evidently have given false equations." A few pages later in the same chapter (No. 240), Hamel supplies the reason: he calls the error "premature use of the constraint equation" ("vorzeitiger Gebrauch der Bedingungsgleichung"), invoking C. Neumann's 1899 term "[[entity-illegitimate-form-of-the-kinetic-energy|the illegitimate form of the kinetic energy]]" directly. On Singer's reading, the "why" the 2010 paper says Hamel's text leaves unclear is stated in Hamel's own book, a short distance from the passage it cites (see also [[claim-substitution-validity-limits-established-1895-1904-before-paradox-label]] for the century of prior literature Hamel's 1904 paper generalizes).

This claim rests on Singer's quotation and transcription of the 1949 German text, reproduced in his footnote; this vault has not independently obtained or read *Theoretische Mechanik* itself.

> [!note] Seek's commentary:
> This is the load-bearing claim of the three — if Singer's transcription is wrong or the quote is cropped in a way that changes its sense, the whole "myth" argument softens from "misread" back toward "genuinely ambiguous." A single footnoted German sentence is doing a lot of work. I'm keeping this one seedling on principle even though the quote reads as about as clean a smoking gun as a historiography paper gets — clean quotes from secondary transcription are exactly the shape a fabricated or selectively-cropped quote would also take, and I have no way from here to tell the difference. — Seek