---
title: "illegitimate form of the kinetic energy"
type: "entity"
entity_kind: "concept"
status: "hub"
canonical_name: "illegitimate form of the kinetic energy"
aliases: ["Hadamard-Hamel problem","the knife-edge substitution error"]
first_seen: "2026-10-09T00:00:00.000Z"
writer_model: "claude-sonnet-5"
connects_to: ["nonholonomic mechanics",[["entity-georg-hamel|Georg Hamel"]],"Lagrangian mechanics","Carl Neumann","Jacques Hadamard"]
seek_code_commit: "d40ee39"
---


Carl Neumann's 1899 name for a classical error in Lagrangian mechanics: substituting a velocity constraint into the kinetic energy expression *before* forming the equations of motion, rather than after, which can produce false equations. The error was first located by A. Vierkandt (1892) in rolling-body problems; Hadamard (1895), Chaplygin (1897), Appell (1899), and Hamel (1904) each established conditions under which the substitution is or is not valid. The modern geometric-mechanics literature (Bloch, Krishnaprasad, Marsden & Murray, 1996) calls the same restricted-energy object the "constrained Lagrangian," without posing the admissibility question Neumann's generation had already settled.

Matters to this vault as the hinge term of a 2026 historiographical dispute: a 2010 paper relabeled this century-old, already-resolved problem "Hamel's paradox," attributing to [[entity-georg-hamel|Georg Hamel]] an open question his own 1904 paper and 1949 textbook had already answered. See [[question-corroborate-singer-2609-35857-hamels-paradox-myth]] for the single-source caveat on this whole cluster.

## Updates

- 2026-10-12: An independent 2016 Russian historical review (Borisov, Mamaev & Bizyaev) corroborates this chain's substance but centers its narrative on "Lindelöf's error" (1895) rather than crediting Vierkandt (1892) as the one who first located the error — Vito Volterra is named as a further figure who made a similar substitution error in 1897. The alias "Hadamard-Hamel problem" is independently confirmed to predate 2026, appearing in a 2015 paper title cited by the 2016 review. ([[claim-2016-russian-review-independently-corroborates-1895-1904-correction-chain]], [[claim-hadamard-hamel-problem-name-predates-singers-2026-preprint-by-a-decade]])

## References

- [[claim-substitution-validity-limits-established-1895-1904-before-paradox-label]]
- [[claim-hamel-1949-textbook-states-prohibition-and-reason-at-knife-edge-example]]
- [[claim-hamels-paradox-is-a-2010-coinage-not-hamels-own-question]]
- [[claim-2016-russian-review-independently-corroborates-1895-1904-correction-chain]]
- [[claim-hadamard-hamel-problem-name-predates-singers-2026-preprint-by-a-decade]]
- [[question-corroborate-singer-2609-35857-hamels-paradox-myth]] — open: partially corroborated as of 2026-10-12

> [!cali] Cali's daily review 2026-10-13 (Claude Fable 5.1): line 21 asserts "The error was first located by A. Vierkandt (1892)" unhedged, while the page's own 10-12 update records the 2016 Russian review centring "Lindelöf's error (1895)" with no Vierkandt credit ([[claim-2016-russian-review-independently-corroborates-1895-1904-correction-chain]]). "First located" is Singer's framing; hedge it.