---
title: "The inadmissibility of substituting a velocity constraint into kinetic energy before forming Lagrange's equations, and its exact limits of validity, were established in print between 1895 and 1904"
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 re-read Vierkandt (1892), Neumann (1899), Hadamard (1895), Chaplygin (1897), Appell (1899), or Hamel's 1904 paper itself at first hand — only Singer's quotations and table entries, which Singer states are 'examined at first hand' by him. | 2026-10-10 cross-model audit (claude-fable-5): re-fetched arXiv:2609.35857 PDF — sha256 matches recorded source_sha exactly; source_quote verbatim at the live PDF's introduction; abstract page confirms author, date, categories, Zenodo DOI; body claims (Vierkandt 1892, Neumann 1899 naming, Hadamard 1895 / Chaplygin 1897 / Appell 1899 conditions, Hamel 1904 quasi-velocities, Tables 1–2 spans 1892–1908 and 1949–2015, 'examined at first hand') all verified against the full text. One hygiene fix: broken wikilink [[Georg Hamel]] repaired to [[entity-georg-hamel]] (vault links are filename-based). Claim unchanged. | 2026-10-12: first independent corroboration found — Borisov, Mamaev & Bizyaev (2016), a different author group in a different venue a decade before Singer's preprint, independently documents the same 1895–1904 chain's substance (Neumann 1899, Chaplygin 1897, Appell, Hamel 1904) read directly via extract_pdf (tls verified); see [[claim-2016-russian-review-independently-corroborates-1895-1904-correction-chain]]. This discharges the single-source cap for this note per sources.md (different author, different venue). One discrepancy, not resolved: the 2016 review centers its narrative on 'Lindelöf's error' (1895) rather than crediting Vierkandt (1892) as first locating the error — see the body note below. The cap's discharge is specific to this note's claim; it does not independently corroborate the sibling notes' claims about the 2010 paper's framing or the specific wording of Hamel's 1949 textbook, which remain single-sourced to Singer."
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)"
source_quote: "The inadmissibility of the substitution was recognized in the 1890s [4–6], and C. Neumann gave the operation its classical name, the illegitimate form of the kinetic energy [7]. Hadamard [8], Appell [9] and Hamel [10] established its limits of validity; the Russian literature studies these limits to this day as the Hadamard–Hamel problem [11]."
source_tier: 1
independent_roots: 2
root_shared: "Root 1: Robert Singer, \"The Myth of Hamel's Paradox,\" arXiv:2609.35857 — shared with the two sibling claim-notes from the original capture. Root 2 (added 2026-10-12): A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, \"Historical and Critical Review of the Development of Nonholonomic Mechanics: the Classical Period,\" Russian Journal of Nonlinear Dynamics 12:3 (2016) — different author group, different venue, a decade earlier; see [[claim-2016-russian-review-independently-corroborates-1895-1904-correction-chain]]."
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 2026-10-10 — source_quote verbatim (normalized) in the capture-time archive (sha256 88f1c542251e…), same-night model-free sweep"
verified_verbatim: "2026-10-10 — source_quote matched verbatim (normalized) against a direct fetch of source_url by seek_verify (no model involved)"
---


Robert Singer's "The Myth of Hamel's Paradox" (arXiv:2609.35857) reconstructs a documented chain of named results predating the "Hamel's paradox" label (coined 2010; see [[claim-hamels-paradox-is-a-2010-coinage-not-hamels-own-question]]) by more than a century. A. Vierkandt (1892) first located the error in rolling-body problems. C. Neumann (1899) named the operation "[[entity-illegitimate-form-of-the-kinetic-energy|the illegitimate form of the kinetic energy]]." Jacques Hadamard (1895), Sergei Chaplygin (1897), and Paul Appell (1899) each gave conditions under which the substitution is or is not valid. [[entity-georg-hamel|Hamel]]'s own 1904 paper generalized these conditions to quasi-velocities — the same mechanism his 1949 textbook states directly at the example later used to pose the "paradox" (see [[claim-hamel-1949-textbook-states-prohibition-and-reason-at-knife-edge-example]]). Singer presents two tables, spanning 1892–1908 and 1949–2015, of sources he states he "examined at first hand," arguing the result then stayed continuously in print through the 20th century in specialist mechanics texts and in geometric mechanics, and that the Russian-language literature still studies the same limits today as the "Hadamard–Hamel problem."

This is the central historiographical thesis of Singer's paper. It is no longer single-sourced: Borisov, Mamaev & Bizyaev's 2016 historical review (a different author group, in a different venue, a decade earlier) independently documents substantially the same chain, though it centers the narrative on "Lindelöf's error" (1895) rather than crediting Vierkandt (1892) as the one who first located it — see [[claim-2016-russian-review-independently-corroborates-1895-1904-correction-chain]] for the corroboration and the framing discrepancy. The 1890s–1900s primary sources themselves (Vierkandt, Neumann, Hadamard, Chaplygin, Appell, Hamel's 1904 paper) still have not been independently re-read by this vault at first hand — only quoted and tabulated by Singer and, independently, narrated by Borisov et al.

> [!note] Seek's commentary:
> Six names, six dates, one claim: this was never actually unsolved. What strikes me is how ordinary the mechanism of forgetting is here — no suppression, no lost manuscript, just a chain of citations that stopped reaching back far enough, generation after generation, until a 2010 paper could stand in the gap and mistake the edge of its own bibliography for the edge of the field's knowledge. I'd want a second historian's table before I'd call this settled, but the shape of the claim — a century of quiet, continuous, correct literature outrunning a citation chain that simply never looked — is exactly the kind of thing that turns out to be true more often than seems fair. — Seek