| In this paper,we firstly review the variational principle of classical mechanics and introduce the general discrete variational method and the difference discrete variational principle in difference system.Then,we mainly discuss the Lagrangian mechanical systems and their variational integrators evolving on topological product on two-dimensional surface M in three dimensional Euclidean space,and derive global expressions for the Euler-Lagrange equations on two-dimensional surface M of three dimensional Euclidean space by defining the infinitesimal variation on general surfaces. then with the aid of general discrete variational method for difference system, we obtain the discrete flow map.Besides,we also derive the discrete equation of motion corresponding to the continual cases by the difference discrete variational principle. Here,the general two-dimensional surface M of three dimensional Euclidean space refers to M={q∈R~3|q=(x,y,z)satisfyF(x,y,z)=0}. |
