The C.Neumann System For The Second-Order Complete Hierarchy

In this paper, the Neumann system and the evolution equation hierarchy associated with the operator L=-(?)~2-iw(?)-i(?)w+u are discussed. On the constraint surfaceΓ, the relations between the potential and the eigenvector are obtained. Then, based on the Euler-Lagrange equations and Legendre transformations, a reasonable Jacobi-Ostrogradsky coordinate system has been found, and it is equal to the real hamiltionian canonical coordinate system. Moreover, using the nonlinearization of Lax pairs and the Moser constraint method, we transform the Neumann system into a finite-dimensional integrable Hamiltonian system in the Liouville sense.