... 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 109by John William Strutt Baron Rayleigh - 1894 - 984 pagesFull view - About this book
| 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... | |
| 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... | |
| John William Strutt Baron Rayleigh - Sound - 1894 - 984 pages
...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... | |
| 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... | |
| ...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... | |
| |