Abstract
AbstractIn this chapter, symplectic approaches for the finite-dimensional Hamiltonian systems are discussed. Firstly, the foundations of the symplectic method are reviewed, which include the symplectic map, the symplectic matrix, the symplectic structure, and so on. Then, two typical symplectic discretization methods are presented. One is the symplectic Runge–Kutta method and another is the splitting/composition method. With these foundations, some research progresses on the applications of the symplectic approach, including the symplectic precise integration of folding and unfolding processes of undercarriage and the symplectic Runge–Kutta method for aerospace dynamics problems are given.
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