一个膺三阶辛积分器  

A Pseudo Third Order Symplectic Integrator

作　　者：刘福窑[1] 伍歆[2] 陆本魁[1] 

机构地区：[1]中国科学院紫金山天文台 [2]南昌大学理学院,南昌330047

出　　处：《天文学报》2004年第4期402-412,共11页Acta Astronomica Sinica

基　　金：国家自然科学青年基金(10303001)资助

摘　　要：在太阳系动力学中,辛积分器已成为研究哈密顿系统的长期定性演化的最佳工具.对于可积分离的哈密顿系统H=H0+∑i=1N∈iHi(∈≤1),构造了一个膺三阶辛积分器.它大约相当于Wisdom-Holman二阶辛积分器的一次校正或Forest-Ruth四阶辛算法的精度.此外,含力梯度的辛算法也适合处理哈密顿系统H=Ho(q,P)+∈H1(q),其精度好于原辛积分器,但不优越于相应膺高阶辛积分器.A symplectic integrator is viewed as promise of being a valuable tool in the numerical exploration of planetary and satellite n-body systems in the solar system dynamics. For a separable Hamiltonian system of the form H = H0 + ∑i=1N∈Hi(∈ ≤ 1), a pseudo-third-order symplectic integrator is constructed, which is shown to be almost equivalent to the first order corrector of the second symplectic integrator or the fourth order symplectic integrator of Forest and Ruth. In addition, symplectic integrator with force gradients can be applied to the Hamiltonian in the manner H = H0(q,p) + ∈H1(q). As to the precision, the modified symplectic integrator is superior to the orginal one but no better than the corresponding pseudo-high-order one.

关 键 词：辛算法 哈密顿系统 可积 四阶 二阶 高阶 梯度 积分器 校正 

分 类 号：P185[天文地球—天文学] O175[理学—数学]