- 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。
In mathematics, a symplectic manifold is a smooth manifold, M, equipped with a closed nondegenerate differential 2-form, ω, called the symplectic form. The study of symplectic manifolds is called symplectic geometry or symplectic topology.