keynote:lesson06
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| ===== 变分问题的欧拉方程 ===== | ===== 变分问题的欧拉方程 ===== | ||
| * 由预备定理可知：<jsmath>F_y-\frac{d}{dx}F_y'=0,\alpha \leq x\leq\beta</jsmath> | * 由预备定理可知：<jsmath>F_y-\frac{d}{dx}F_y'=0,\alpha \leq x\leq\beta</jsmath> | ||
| - | * 如果展开dF<sub>y'/</sub>dx\[ F_y-\frac{{\partial}^2 F}{\partial x\partial y}-\frac{{\partial}^2 F}{\partial y\partial y'}y'-\frac{{\partial}^2 F}{\partial y'\partial x}y''=0 \] | + | * 如果展开dF<sub>y'/</sub>dx\[ F_y-\frac{{\partial}^2 F}{\partial x\partial y}-\frac{{\partial}^2 F}{\partial y\partial y'}y'-\frac{{\partial}^2 F}{\partial y'\partial y'}y''=0 \] |
| * 其中F(x,y,y’)必须具有二阶偏导数，y(x)也必须具有二阶偏导数。 | * 其中F(x,y,y’)必须具有二阶偏导数，y(x)也必须具有二阶偏导数。 | ||
| <note>**由此把变分问题转化为微分方程求解**</note> | <note>**由此把变分问题转化为微分方程求解**</note> | ||
| + | <note important> Revised by 王益文, 10921064 </note> | ||
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| --- //[[qiuweiwei@zju.edu.cn|邱炜伟]] 2010/04/12 20:53// | --- //[[qiuweiwei@zju.edu.cn|邱炜伟]] 2010/04/12 20:53// | ||
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