An algebraic approach to Hamilton's canonical equations

Hamilton's canonical equations play important roles in the analysis and control of nonlinear systems. How ever, it is difficult to obtain their analytic solutions because they are nonlinear ordinary differential equations. In this paper, we introduce a new algebraic solution method for the equations in the case that the Hamiltonian is a polynomial of the costate with coefficients consisting of the rational functions of the state and the meromorphic functions of time, and the costate is a function of the state and time. By our method, for some classes of problems, analytic solutions of the equation can be obtained by solving only algebraic equations.