\(t=\left(\frac{G}{w}\right)^{2}\) |
(26) |
\(t^{-1}=\left(\frac{w}{G}\right)^{2}\) |
(27) |
\(H\sqrt{t}=\frac{\text{G\ H}}{w}\) |
(28) |
\(H^{2}t=\left(\frac{\text{G\ H}}{w}\right)^{2}\) |
(29) |
\(\frac{\text{dw}}{\text{dt}}=\frac{d}{\text{dt}}\left(\frac{G}{\sqrt{t}}\right)=\frac{d}{\text{dt}}\left(\text{G\ }t^{-1/2}\right)=-\frac{1}{2}\text{G\ }t^{-\frac{3}{2}}\) |
(30) |
\(dw=-\frac{1}{2}\text{G\ }t^{-\frac{3}{2}}\text{\ dt}=-\frac{1}{2}\left(\text{G\ }t^{-\frac{1}{2}}\right)^{3}\frac{1}{G^{2}}\text{\ dt}=-\frac{w^{3}}{2G^{2}}\text{\ dt}\) |
(31) |
\(dt=-\frac{2G^{2}}{w^{3}}\text{dw}\) |
(32) |