| 钟万勰,孙雁.短波近似的保辛算法[J].计算力学学报,2008,25(1):1~7 |
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| 短波近似的保辛算法 |
| Symplectic conservative integration for short-wave approximation |
| 修订日期：2005-08-26 |
| DOI：10.7511/jslx20081004 |
| 中文关键词: 保辛,坐标正则变换,混合能密度,短波近似 |
| 英文关键词:symplectic conservation,coordinate canonical transformation,mixed energy density,WKBJ approximation |
| 基金项目:国家自然科学基金 |
| 钟万勰 孙雁 |
| 大连理工大学工程力学系，上海交通大学工程力学系 辽宁大连116023，上海交通大学工程力学系，上海200030，上海200030 |
| 摘要点击次数: 1965 |
| 全文下载次数: 34 |
| 中文摘要: |
| WKBJ短波近似是最常用的有效求解方法之一。保守体系的微分方程可用Hamilton体系的方法描述,其特点是保辛。保辛给出保守体系结构最重要的特性。但WKBJ短波近似却未曾考虑保辛的问题。WKBJ近似可用自变量坐标变换,然后再给出其保辛摄动。数值例题展示了本文变换保辛算法的有效性。 |
| 英文摘要: |
| All approximations for a conservative system should be symplectic conservative.The traditional perturbation approaches are based on the Taylor series expansion which uses additional operation.The addition for a transfer symplectic matrix is not symplectic conserved,however,the symplectic matrices are conserved under multiplication.The symplectic conservative perturbation for a conservative system can use the canonical transformation method.However,the well-known WKBJ short wave-length approximation is not symplectic conservative.The former paper[7] has not taken the coordinate transformation into consideration,more steps of integration are necessary.The method of coordinate transformation and the polynomial approximation of mixed energy density are applied in this paper,and then the solution of unknown state vector is solved,which needs far fewer steps of integration.Numerical results demonstrate the effectiveness of the present method. |
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