"Hamel's paradox" is a 2010 coinage by Udwadia and Wanichanon, not a problem Hamel himself posed or left open

physicsclassical-mechanicsnonholonomic-systemshistory-of-sciencehistoriographypriority-disputelagrangian-mechanics

In 2010, Firdaus E. Udwadia and Thanapat Wanichanon published "Hamel's Paradox and the Foundations of Analytical Dynamics" (Applied Mathematics and Computation), introducing the name for a known failure mode: substituting a velocity constraint into the kinetic energy expression before forming Lagrange's equations, rather than after, which can produce false equations of motion (the classic case is a knife-edge or rolling-disk constraint). The 2010 paper framed this as "a paradox posed by Hamel in his 1949 book" and stated that Hamel's text left open both why the substitution fails and under what conditions it would.

A 2026 preprint by Robert Singer, "The Myth of Hamel's Paradox" (arXiv:2609.35857), argues both characterizations are incorrect. On Singer's reading, Hamel's own 1949 textbook already states the mechanism a few pages after the passage the 2010 paper cites (see claim-hamel-1949-textbook-states-prohibition-and-reason-at-knife-edge-example), and the conditions of validity had been established decades earlier in the published literature (see claim-substitution-validity-limits-established-1895-1904-before-paradox-label). The shape of the error, per Singer, is a priority dispute running in reverse: instead of a result being credited to someone other than its originator, a question is attributed to a figure who had already answered it. Y.H. Chen (2013) and T. Wanichanon & H. Cho (2024) each continued the "Hamel's paradox" framing in later papers; Singer states neither reaches back into the 1890s–1900s literature.

This note rests on a single unrefereed preprint quoting the 2010 paper by page number; the 2010 paper itself has not been read at first hand by this vault.