准坐标下非完整力学系统的lie对称性和守恒量

Abstract

Abstract:

ＴｈｉｓｐａｐｅｒｉｎｖｏｌｖｅｓＬｉｅｓｙｍｍｅｔｒｉｅｓａｎｄｃｏｎｓｅｒｖａｔｉｏｎｌａｗｓｏｆｎｏｎｈｏｌｎｏｍｉｃｓｙｓｔｅｍｓｉｎｔｅｒｍｓｏｆｑｕａｓｉｃｏｏｒｄｉｎａｔｅｓ．ＷｅｓｔｕｄｉｅｄｔｗｏｋｉｎｄｓｏｆｐｒｏｂｌｅｍｓｏｎＬｉｅｓｙｍｍｅｔｒｉｅｓａｎｄｃｏｎｓｅｒｖｅｄｑｕａｎｔｉｔｉｅｓ．ＯｎｅｉｓｔｈｅｄｉｒｅｃｔｐｒｏｂｌｅｍｏｆＬｉｅｓｙｍｍｅｔｒｉｅｓ：ｆｉｎｄｉｎｇｏｕｔｔｈｅｃｏｒｒｅｓｐｏｎｄｉｎｇｃｏｎｓｅｒｖｅｄｑｕａｎｔｉｔｙａｃｃｏｒｄｉｎｇｔｏａｇｉｖｅｎＬｉｅｓｙｍｍｅｔｒｙ．Ｗｅｇｉｖｅｓｔｈｅｄｅｆｉｎｉｔｉｏｎｏｆｔｈｅｉｎｆｉｎｉｔｅｓｈｍａｌｇｅｎｅｒａｔｏｒｆｏｒｔｈｅｎｏｎｈｏｌｏｎｏｍｉｃｓｙｓｔｅｍｓｉｎｔｅｒｍｓｏｆｑｕａｓｉｃｏｏｒｄｉｎａｔｅｓ．Ｕｓｉｎｇｔｈｅｉｎｖａｒｉａｎｃｅｏｆｔｈｅｏｒｄｉｎａｒｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｕｎｄｅｒｔｈｅｉｎｆｉｎｉｔｅｓｉｍａｌｔｒａｎｓｆｏｒｍａｔｉｏｎｓ，ｅｓｔａｂｌｉｓｈｅｓｔｈｅｄｅｔｅｒｍｉｎｉｎｇｅｑｕａｔｉｏｎｓｏｆｔｈｅＬｉｅｓｙｍｍｅｔｒｉｅｓ．Ｏｂｔａｉｎｓｔｈｅｓｔｒｕｃｔｕｒｅｅｑｕａｔｉｏｎａｎｄｃｏｎｓｅｒｖｅｄｑｕａｎｔｉｔｉｅｓ．ＴｈｅａｎｏｔｈｅｒｋｉｎｄｓｏｆｐｒｏｂｌｅｍｉｓｃａｌｌｅｄｔｈｅｉｎｖｅｒｓｅｐｒｏｂｌｅｍｏｆＬｉｅｓｙｍｍｅｔｒｉｅｓ：ｆｉｎｄｏｕｔｔｈｅｃｏｒｒｅｓｐｏｎｄｉｎｇＬｉｅｓｙｍｍｅｔｒｙａｃｃｏｒｄｉｎｇｔｏａｋｎｏｗｎｃｏｎｓｅｒｖｅｄｑｕａｎｔｉｔｙ．Ｇｉｖｅｓａｎｅｘａｍｐｌｅｔｏｉｌｌｕｓｔｒａｔｅｔｈｅａｐｐｌｉｃａｔｉｏｎｏｆｔｈｅｒｅｓｕｌｔ．

Key words: Ａｎａｌｙｔｉｃａｌｍｅｃｈａｎｉｃｓ, Ｑｕａｓｉｃｏｏｒｄｉｎａｔｅ, Ｌｉｅｓｙｍｍｅｔｒｙ, Ｃｏｎｓｅｒｖｅｄｑｕａｎｔｉｔｙ, Ｎｏｎｈｏｌｏｎｏｍｉｃｍｅｃｈａｎｉｃａｌｓｙｓｔｅｍ．

CLC Number:

FU Jing-Li, LIU Rong-Mo. Lie Symmetries and conservd Quantilities of Nonholonomic Mechanical System in term of Quasi-coordinate[J].Acta mathematica scientia,Series A, 2000, 20(1): 63-69.

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References

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[1]	LIANG Jing-Hui. Lie Symmetries and Conserved Quantities of Nonholonomic Systems of Non-Chetaev's Type with Unilateral Constraints in phase Space [J]. Acta mathematica scientia,Series A, 2001, 21(2): 185-190.
[2]	Zhang Yi \| Mei Fengxiang. Lie Symmetries and Conserved Quantities of Nonholonomic Mechanical Systems with Unilateral Constraints [J]. Acta mathematica scientia,Series A, 2000, 20(1): 95-100.

Lie Symmetries and conservd Quantilities of Nonholonomic Mechanical System in term of Quasi-coordinate

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