legendre transformation meaning in English
勒壤得转换
勒让德变换
Examples
- In order to avoid the difficulty in computing the general inverse of flexible matrix in legendre transformation , this paper studies the mixed coordinates formulation for some quadrilateral plate bending elements instead of fully formulating in ( e , n ) plane for their original plane elasticity elements
为了克服legendre变换中对单元柔度阵求广义逆的困难，对于原平面弹性单元是在参考坐标系中列式的情形，本文研究了在弯矩函数空间的混合坐标列式。 - In this paper , we convert the complex third order eigenvalue problems into the real third order eigenvalue problems . then , based on the euler - lagrange equation and legendre transformation , a reasonable jacobi - ostrogredsky coordinate system have been found , then using nonlinear method , the lax pairs of the real bargrnann and neumann system are nonlinearized , so as to be a new finite - dimensional integrable hamilton system in the liouville sense is generated . moreover , the involutive representations of the solution for the evolution equations are obtained
本文将复的三阶特征值问题转化为实的三阶特征值问题，利用euler - lagrange方程和legendre变换，找到一组合理的实的jacobi - ostrogredsky坐标系，从而找到与之相关的实化系统，再利用曹策问教授的非线性化方法，分别将三阶特征值问题及相应的lax对进行非线性化，从而得到bargmann势和neumann势约束系统，并证明它们是liouville意义下的完全可积系统，进而给出了bargmann系统和neumann系统的对合解。 - In this paper , by means of the euler systems on the symplectic manifold , the bargmann system and the neumann system for the 4f / lorder eigenvalue problems : are gained . then the lax pairs for them are nonlinearized respectively under the bargmann constraint and the neumann constraint . by means of this and based on the euler - lagrange function and legendre transformations , the reasonable jacobi - ostrogradsky coordinate systems are found , which can also be realized
本文主要通过流形上的euler系统，讨论四阶特征值问题所对应的bargmann系统和neumann系统，借助于lax对非线性化及euler - lagrange方程和legendre变换，构造一组合理的且可实化的jacobi - ostrogradsky坐标系? hamilton正则坐标系，将由lagrange力学描述的动力系统转化为辛空间( r ~ ( 8n ) ， )上的hamillton正则系统。