Projected Runge-Kutta methods for constrained Hamiltonian systems

被引：0

作者：

Yi WEI ^{[1
]}

Zichen DENG ^{[2
]}

Qingjun LI ^{[2
]}

Bo WANG ^{[3
]}

机构：

[1] Department of Applied Mathematics,Northwestern Polytechnical University

[2] Department of Engineering Mechanics,Northwestern Polytechnical University

[3] Mechanical and Aerospace Engineering,Oklahoma State University

来源：

AppliedMathematicsandMechanics(EnglishEdition) | 2016年 / 37卷 / 08期

基金：

中国国家自然科学基金; 中央高校基本科研业务费专项资金资助;

关键词：

projected Runge-Kutta(R-K) method; differential-algebraic equation(DAE); constrained Hamiltonian system; energy and constraint preservation; constraint violation;

D O I：

暂无

中图分类号：

O241.8 [微分方程、积分方程的数值解法];

学科分类号：

摘要：

Projected Runge-Kutta(R-K) methods for constrained Hamiltonian systems are proposed.Dynamic equations of the systems,which are index-3 differential-algebraic equations(DAEs) in the Heisenberg form,are established under the framework of Lagrangian multipliers.R-K methods combined with the technique of projections are then used to solve the DAEs.The basic idea of projections is to eliminate the constraint violations at the position,velocity,and acceleration levels,and to preserve the total energy of constrained Hamiltonian systems by correcting variables of the position,velocity,acceleration,and energy.Numerical results confirm the validity and show the high precision of the proposed method in preserving three levels of constraints and total energy compared with results reported in the literature.

引用

页码：1077 / 1094

页数：18

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