Hamilton方程的变分离散方法

Variational Discrete Method for Hamiltonian Systems

讨论了经典Hamilton系统的变分原理 ,通过离散方程所对应的Lagrangian函数的方法 ,由离散的变分原理得到了一系列的辛差分算法 ,其中包括传统的辛格式 ,如 :辛Euler格式和中点格式 .

The variational principle of the classical Hamiltonian systems is discussed. Based on the discrete variational principle, a series of symplectic difference algorithms, which include some widely used symplectic schemes such as the symplectic Euler scheme and the midpoint scheme are constructed by discreting the corresponding Lagramgian functions.