Search

1.2: Розширення до 3-D корпусу
https://ukrayinska.libretexts.org/%D0%86%D0%BD%D0%B6%D0%B5%D0%BD%D0%B5%D1%80%D0%BD%D0%B0/%D0%9C%D0%B0%D1%88%D0%B8%D0%BD%D0%BE%D0%B1%D1%83%D0%B4%D1%83%D0%B2%D0%B0%D0%BD%D0%BD%D1%8F/%D0%91%D1%83%D0%B4%D1%96%D0%B2%D0%B5%D0%BB%D1%8C%D0%BD%D0%B0_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D1%96%D0%BA%D0%B0_(Wierzbicki)/01%3A_%D0%9F%D0%BE%D0%BD%D1%8F%D1%82%D1%82%D1%8F_%D1%88%D1%82%D0%B0%D0%BC%D1%83/1.02%3A_%D0%A0%D0%BE%D0%B7%D1%88%D0%B8%D1%80%D0%B5%D0%BD%D0%BD%D1%8F_%D0%B4%D0%BE_3-D_%D0%BA%D0%BE%D1%80%D0%BF%D1%83%D1%81%D1%83
\[ du_i(x_i) = \frac{\partial u_i}{ \partial x_1} d x_1 + \frac{\partial u_i}{ \partial x_2} d x_2 + \frac{\partial u_i}{ \partial x_3} d x_3 = \sum_{j=1}^3 \frac{\partial u_i}{ \partial x_j} d x_j\] ...\[ du_i(x_i) = \frac{\partial u_i}{ \partial x_1} d x_1 + \frac{\partial u_i}{ \partial x_2} d x_2 + \frac{\partial u_i}{ \partial x_3} d x_3 = \sum_{j=1}^3 \frac{\partial u_i}{ \partial x_j} d x_j\] \[\frac{\partial u_i}{ \partial x_j} = \frac{1}{2} \left(\frac{\partial u_i}{ \partial x_j} + \frac{\partial u_j}{ \partial x_i}\right) + \left(\frac{1}{2}\frac{\partial u_i}{ \partial x_j} - \frac{\partial u_j}{ \partial x_i}\right) \label{1.2.5}\]