Structure-preserving properties of Strmer-Verlet scheme for mathematical pendulum

作     者：Weipeng HU Mingzhe SONG Zichen DENG 

作者机构：School of MechanicsCivil Engineering and ArchitectureNorthwestern Polytechnical UniversityXi'an 710072China State Key Laboratory of Structural Analysis of Industrial EquipmentDalian University of TechnologyDalian 116023Liaoning ProvinceChina 

出 版 物：《Applied Mathematics and Mechanics(English Edition)》 (应用数学和力学（英文版）)

年 卷 期：2017年第38卷第9期

页      面：1225-1232页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：the National Natural Science Foundation of China(Nos.11672241,11372253,and 11432010) the Astronautics Supporting Technology Foundation of China(No.2015-HT-XGD) the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment(Nos.GZ1312 and GZ1605) 

主　　题：Strmer-Verlet scheme symplectic mathematical pendulum structure-preserving Hamiltonian system phase correction 

摘      要：The structure-preserving property, in both the time domain and the frequency domain, is an important index for evaluating validity of a numerical method. Even in the known structure-preserving methods such as the symplectic method, the inherent conser- vation law in the frequency domain is hardly conserved. By considering a mathematical pendulum model, a Stormer-Verlet scheme is first constructed in a Hamiltonian frame- work. The conservation law of the StSrmer-Verlet scheme is derived, including the total energy expressed in the time domain and periodicity in the frequency domain. To track the structure-preserving properties of the Stormer-Verlet scheme associated with the con- servation law, the motion of the mathematical pendulum is simulated with different time step lengths. The numerical results illustrate that the StSrmer-Verlet scheme can preserve the total energy of the model but cannot preserve periodicity at all. A phase correction is performed for the StSrmer-Verlet scheme. The results imply that the phase correction can improve the conservative property of periodicity of the Stormer-Verlet scheme.