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Books Books 1 - 5 of 5 on ... essentially real. It is remarkable that both Lagrange and Laplace fell into the....  
" ... essentially real. It is remarkable that both Lagrange and Laplace fell into the error of supposing that equality among roots necessarily implies terms in the solution of the form te xt (or tcospt), and therefore that for stability the roots must be... "
The Theory of Sound - Page 109
by John William Strutt Baron Rayleigh - 1894 - 984 pages
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Treatise on Natural Philosophy, Volume 1, Issue 1

William Thomson Baron Kelvin, Peter Guthrie Tait - Calculators - 1879
...real, and whether it be positive or negative the ratios <*,/,, *g/,> etc., are essentially real. It is remarkable that both Lagrange and Laplace fell...that equality among roots necessarily implies terms in the solution of the form tt** (or t cos pt), and therefore that for stability the roots must be...
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TREATISE ON NATURAL PHILOSOPHY

SIR WILLIAM THOMSON, PETER GUTHRIE TAIT - 1888
...essentially real, and whether it be positive or negative the ratios aja l9 ajct,^ etc., are essentially real. It is remarkable that both Lagrange and Laplace fell...that equality among roots necessarily implies terms in the solution of the form te xt (or tcospt), and therefore that for stability the roots must be all...
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The theory of sound, Volume 1

Baron John William Strutt Rayleigh - Sound - 1894
...first term ultimately acquires the preponderance, inasmuch as At*-' : Be*'' = (A/B) 'A. -*'. In general, unstable equilibrium when disturbed infinitesimally...equality among roots necessarily implies terms containing < as a factor1. The analytical theory of the general case (where the co-ordinates are not normal) has...
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The Theory of Sound, Volume 1

John William Strutt Baron Rayleigh - Sound - 1894 - 984 pages
...reduction to normal co-ordinates allows us readily to trace what occurs when two of the values of 2 become equal. It is evident that there is no change...by Routh2.] 88. The interpretation of the equations of motion leads to a theorem of considerable importance, which may be thus stated4. The period of a...
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Treatise on Natural Philosophy, Part 1

William Thomson, William Thomson, Peter Guthrie Tait - 2010 - 526 pages
...real, and whether it be positive or negative the ratios ,/a,, ,/a,, etc., are essentially real. It is remarkable that both Lagrange and Laplace fell...that equality among roots necessarily implies terms in the solution of the form <fw (or tcospt), and therefore that for stability the roots must be all...
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