The reduction to-normal co-ordinates allows us readily to trace what occurs when two of the values of n1 become equal. It is evident that there is no change of form. The spherical pendulum may be referred to as a simple example of equal roots. It is remarkable... The Theory of Sound - Page 109by John William Strutt Baron Rayleigh - 1894 - 984 pagesFull view - About this book
| 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... | |
| 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... | |
| Baron John William Strutt Rayleigh - Sound - 1894
...reduction to normal co-ordinates allows us readily to trace what occurs when two of the values of n- **become equal. It is evident that there is no change...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 - Science - 1945 - 520 pages
...reduction to-normal co-ordinates allows us readily to trace what occurs when two of the values of n' **become equaL It is evident that there is no change...roots necessarily implies terms containing t as a** factor'. The analytical theory of the general case (where the co-ordinates are not normal) has been... | |
| 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... | |
| |