illegitimate form of the kinetic energy

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 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