Symmetry of Lagrangians of a holonomic variable mass system

doi:10.1088/1674-1056/21/6/064501

中国物理B ›› 2012, Vol. 21 ›› Issue (6): 64501-064501.doi: 10.1088/1674-1056/21/6/064501

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

Symmetry of Lagrangians of a holonomic variable mass system

吴惠彬, 梅凤翔

Faculty of Science, Beijing Institute of Technology, Beijing 100081, China

收稿日期:2011-11-13 修回日期:2011-12-25 出版日期:2012-05-01 发布日期:2012-05-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10932002 and 10972031) and the Beijing Municipal Key Disciplines Fund for General Mechanics and Foundation of Mechanics.

Symmetry of Lagrangians of a holonomic variable mass system

Wu Hui-Bin(吴惠彬)^† and Mei Feng-Xiang(梅凤翔)

Faculty of Science, Beijing Institute of Technology, Beijing 100081, China

Received:2011-11-13 Revised:2011-12-25 Online:2012-05-01 Published:2012-05-01
Contact: Wu Hui-Bin E-mail:huibinwu@bit.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10932002 and 10972031) and the Beijing Municipal Key Disciplines Fund for General Mechanics and Foundation of Mechanics.

摘要/Abstract

摘要： The symmetry of Lagrangians of a holonomic variable mass system is studied. Firstly, the differential equations of motion of the system are established. Secondly, the definition and the criterion of the symmetry of the system are presented. Thirdly, the conditions under which there exists a conserved quantity deduced by the symmetry are obtained. The form of the conserved quantity is the same as that of the constant mass Lagrange system. Finally, an example is shown to illustrate the application of the result.

关键词: Holonomic system, variable mass system, symmetry of Lagrangians, conserved quantity

Abstract: The symmetry of Lagrangians of a holonomic variable mass system is studied. Firstly, the differential equations of motion of the system are established. Secondly, the definition and the criterion of the symmetry of the system are presented. Thirdly, the conditions under which there exists a conserved quantity deduced by the symmetry are obtained. The form of the conserved quantity is the same as that of the constant mass Lagrange system. Finally, an example is shown to illustrate the application of the result.

Key words: Holonomic system, variable mass system, symmetry of Lagrangians, conserved quantity

中图分类号: (Lagrangian and Hamiltonian mechanics)

45.20.Jj

11.30.-j (Symmetry and conservation laws)

吴惠彬, 梅凤翔. Symmetry of Lagrangians of a holonomic variable mass system[J]. 中国物理B, 2012, 21(6): 64501-064501.

Wu Hui-Bin(吴惠彬) and Mei Feng-Xiang(梅凤翔) . Symmetry of Lagrangians of a holonomic variable mass system[J]. Chin. Phys. B, 2012, 21(6): 64501-064501.

参考文献 26

[1]	Santilli R M 1983 Foundations of Theoretical Mechanics/ II (New York: Springer-Verlag)
[2]	Dass T 1966 Phys. Rev. 150 1251
[3]	Djukić Dj S 1974 Arch. Mech. 26 243
[4]	Djukić Dj S and Vujanović B D 1975 Acta Mech. 23 17
[5]	Bahar L Y and Kwatny H G 1987 Int. J. Nonlinear Mech. 22 125
[6]	Sarlet W and Cantrijn F 1981 SIAM Rev. 23 467
[7]	Liu D 1991 Sci. Chin. Ser. A 34 419
[8]	Mei F X 1993 Sci. Chin. Ser. A 36 1456
[9]	Lutzky M 1979 J. Phys. A: Math. Gen. 12 973
[10]	Prince G E and Eliezer C J 1981 J. Phys. A: Math. Gen. 14 587
[11]	Mei F X 2000 Acta Mech. 141 135
[12]	Fu J L and Chen L Q 2003 Phys. Lett. A 317 255
[13]	Chen X W, Li Y M and Zhao Y H 2005 Phys. Lett. A 337 274
[14]	Mei F X 2000 J. Beijing Institute of Technology 9 120
[15]	Wang S Y and Mei F X 2002 Chin. Phys. 11 5
[16]	Fu J L and Chen L Q 2004 Phys. Lett. A 331 138
[17]	Shi S Y and Fu J L 2011 Chin. Phys. B 20 021101
[18]	Jiang W A, Li Z J and Luo S K 2011 Chin. Phys. B 20 030202
[19]	Currie D G and Saletan E J 1966 J. Math. Phys. 7 967
[20]	Hojman S and Harleston H 1981 J. Math. Phys. 22 1414
[21]	Metscherski I A 1952 Works on Mechanics of Body of Variable Mass (Moscow: GTTTL) (in Russian)
[22]	Gantmacher F R and Levin L M 1964 The Fight of Uncontrolled Rockets (New York: The Macmillan Co)
[23]	Yang L W and Mei F X 1989 Mechanics of Variable Mass Systems (Beijing: Beijing Institute of Technology Press) (in Chinese)
[24]	Ge Z M 1997 Advanced Dynamics for Variable Mass Systems (Taipeh: Gah Lih Book Company)
[25]	Mei F X 2000 ASME Appl. Mech. Rev. 53 283
[26]	Zhao Y Y and Mei F X 1999 Symmetries and Invariants of Mechanical Systems (Beijing: Science Press) (in Chinese)

Symmetry of Lagrangians of a holonomic variable mass system

Symmetry of Lagrangians of a holonomic variable mass system

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 26

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Jian Zhang(张健), Yiming Liu(刘一鸣), and Zhanchun Tu(涂展春). Exploring fundamental laws of classical mechanics via predicting the orbits of planets based on neural networks[J]. 中国物理B, 2022, 31(9): 94502-094502.
[2]	王勇, 崔金超, 陈菊, 郭永新. Quasi-canonicalization for linear homogeneous nonholonomic systems[J]. 中国物理B, 2020, 29(6): 64501-064501.
[3]	金世欣, 张毅. Generalized Chaplygin equations for nonholonomic systems on time scales[J]. 中国物理B, 2018, 27(2): 20502-020502.
[4]	宋静, 张毅. Noether symmetry and conserved quantity for dynamical system with non-standard Lagrangians on time scales[J]. 中国物理B, 2017, 26(8): 84501-084501.
[5]	刘世兴, 刘畅, 花巍, 郭永新. Generalized Birkhoffian representation of nonholonomic systems and its discrete variational algorithm[J]. 中国物理B, 2016, 25(11): 114501-114501.
[6]	王琳莉, 傅景礼. Non-Noether symmetries of Hamiltonian systems withconformable fractional derivatives[J]. 中国物理B, 2016, 25(1): 14501-014501.
[7]	夏丽莉, 陈立群, 傅景礼, 吴旌贺. Symmetries and variational calculationof discrete Hamiltonian systems[J]. , 2014, 23(7): 70201-070201.
[8]	金世欣, 张毅. Noether symmetry and conserved quantity for a Hamilton system with time delay[J]. 中国物理B, 2014, 23(5): 54501-054501.
[9]	周燕, 张毅. Noether's theorems of a fractional Birkhoffian system within Riemann–Liouville derivatives[J]. 中国物理B, 2014, 23(12): 124502-124502.
[10]	孙毅, 陈本永, 傅景礼. Lie symmetry theorem of fractional nonholonomic systems[J]. , 2014, 23(11): 110201-110201.
[11]	赵纲领, 陈立群, 傅景礼, 洪方昱. Mei symmetry and conservation laws of discrete nonholonomic dynamical systems with regular and irregular lattices[J]. 中国物理B, 2013, 22(3): 30201-030201.
[12]	陈蓉, 许学军. Conformal invariance, Noether symmetry, Lie symmetry and conserved quantities of Hamilton systems[J]. 中国物理B, 2012, 21(9): 94501-094501.
[13]	崔金超, 韩月林, 贾利群 . A type of conserved quantity of Mei symmetry of Nielsen equations for a holonomic system[J]. 中国物理B, 2012, 21(8): 80201-080201.
[14]	张斌, 方建会, 张伟伟 . Symmetry of Lagrangians of holonomic nonconservative system in event space[J]. 中国物理B, 2012, 21(7): 70208-070208.
[15]	夏丽莉, 陈立群. Noether conserved quantities and Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices[J]. 中国物理B, 2012, 21(7): 70202-070202.