The Formalized Methods And Applications Of Hamilton Canonical System Of Higher Order Differential Equations

Now, the higher order differential equation has become one of the most important means of scientific research, obtain the variables we need by establishing equations which have practical significance, the study of solving higher order differential equations and its related properties has become a crucial issue. At present, in physics, mechanics, mathematics and other scientific research field, Hamiltonian form of differential equations, due to the good symmetry, bring great convenience for solving the equations and discussion the nature of equations, even has become a popular form. However, due to the high order, the problem of solving corresponding Hamilton form of many differential equations has become very difficult. Hamilton is mainly divided into two categories, the infinite dimensional Hamilton form and the finite dimensional Hamilton form. On the basis of the former, this paper mainly makes some brief discussion and study on the infinite Hamilton forms, and gives the Hamilton forms of some types of higher order differential equations and some special form of the higher order differential equationsIn the first chapter, firstly, gives the different definitions of Hamilton system, and generally describes the development and the present situation of Hamilton system, in addition, introduces some new conclusions and the progress about Hamilton form in recent years. Secondly lists different definitions of Hamilton and basic concepts used in this paper; finally gives a brief introduction about the main work of this paper.In the second chapter, a special canonical hamilton form of four order and a class of specific six order differential equations are discussed, proves and gives the canonical Hamilton forms of the four order and six order differential equations. Although, this method is machinery, but to a certain extent, simplifies the solution of the canonical hamilton form of certain types of equations. In addition, the canonical hamilton form given in this chapter is different from those given by other method. so, expands the types of Hamilton formIn the third chapter, do a further understanding on the original algebra raising dimension method, Explore the setting of some special Hamilton matrix, and the types of differential equations corresponding to these setting situations. Gives effective examples. This method will greatly simplify the solution of Hamilton canonical form of some types of differential equationsIn the fourth chapter, summarizing this paper briefly, analyzing the deficiencies and the direction that need to continue to research...