Abstract
A FEW weeks ago you published in a letter from Mr. Heaviside a proof of Lagrange's equations of motion of a system of bodies. I must confess that I in common with others swallowed it, but I have now come to the conclusion that the proof, though doubtless admirable as an example of the power of the “Principle of Activity,” does not prove Lagrange's equations. In fact, if q be a coordinate, q the corresponding velocity, and Q the corresponding force, we have the result for any possible motion of the system. But we are not entitled to equate the quantities in the brackets to zero, for these are not independent of q.The "proof" is, in fact, merely Maxwell's well-known but fallacious proof, simplified by going direct instead of viaHamilton.
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W., R. Proof of Lagrange's Equations of Motion, &c. . Nature 67, 415 (1903). https://doi.org/10.1038/067415b0
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DOI: https://doi.org/10.1038/067415b0
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