Generalized Chaplygin equations for nonholonomic systems on time scales

doi:10.1088/1674-1056/27/2/020502

中国物理B ›› 2018, Vol. 27 ›› Issue (2): 20502-020502.doi: 10.1088/1674-1056/27/2/020502

Generalized Chaplygin equations for nonholonomic systems on time scales

Shi-Xin Jin(金世欣), Yi Zhang(张毅)

1. School of Science, Nanjing University of Science and Technology, Nanjing 210094, China;
2. College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China

收稿日期:2017-07-15 修回日期:2017-10-19 出版日期:2018-02-05 发布日期:2018-02-05
通讯作者: Yi Zhang E-mail:zhy@mail.usts.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11572212 and 11272227) and the Innovation Program for Postgraduate in Higher Education Institutions of Jiangsu Province, China (Grant No. KYLX16-0414).

Generalized Chaplygin equations for nonholonomic systems on time scales

Shi-Xin Jin(金世欣)¹, Yi Zhang(张毅)²

1. School of Science, Nanjing University of Science and Technology, Nanjing 210094, China;
2. College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China

Received:2017-07-15 Revised:2017-10-19 Online:2018-02-05 Published:2018-02-05
Contact: Yi Zhang E-mail:zhy@mail.usts.edu.cn
About author:05.45.-a; 11.10.Ef; 02.30.Hq
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11572212 and 11272227) and the Innovation Program for Postgraduate in Higher Education Institutions of Jiangsu Province, China (Grant No. KYLX16-0414).

摘要/Abstract

摘要： The generalized Chaplygin equations for nonholonomic systems on time scales are proposed and studied. The Hamilton principle for nonholonomic systems on time scales is established, and the corresponding generalized Chaplygin equations are deduced. The reduced Chaplygin equations are also presented. Two special cases of the generalized Chaplygin equations on time scales, where the time scales are equal to the set of real numbers and the integer set, are discussed. Finally, several examples are given to illustrate the application of the results.

关键词: nonholonomic system, generalized Chaplygin equations, time scales

Abstract: The generalized Chaplygin equations for nonholonomic systems on time scales are proposed and studied. The Hamilton principle for nonholonomic systems on time scales is established, and the corresponding generalized Chaplygin equations are deduced. The reduced Chaplygin equations are also presented. Two special cases of the generalized Chaplygin equations on time scales, where the time scales are equal to the set of real numbers and the integer set, are discussed. Finally, several examples are given to illustrate the application of the results.

Key words: nonholonomic system, generalized Chaplygin equations, time scales

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

11.10.Ef (Lagrangian and Hamiltonian approach) 02.30.Hq (Ordinary differential equations)

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.

Shi-Xin Jin(金世欣), Yi Zhang(张毅). Generalized Chaplygin equations for nonholonomic systems on time scales[J]. Chin. Phys. B, 2018, 27(2): 20502-020502.

参考文献 32

[1]	Hilger S 1988 "Ein Mαβkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten", Ph. D. thesis (Universit Würzburg)
[2]	Ahlbrand D, Bohner M and Ridenhour J 2000 J. Math. Anal. Appl. 250 561
[3]	Bohner M and Peterson A 2001 Dynamic Equations on Time Scale:An Introduction with Applications (Boston:Birkhäuser)
[4]	Bohner M and Peterson A 2003 Advances in Dynamic Equations on Time Scales (Boston:Birkhäuser)
[5]	Agarwal R, Martin B, et al. 2004 J. Comput. Appl. Math. 141 1
[6]	Bohner M and Guseinov G S H 2004 Dyn. Sys. Appl. 13 351
[7]	MAtici F, Biles D C and Lebedinsky A 2006 Math. Comput. Definition 43 718
[8]	Zhang H T and Li Y K 2009 Commun. Nonlinear Sci. Numer. Simul. 14 19
[9]	Abdeljawad T, Jarad F and Baleanu D 2009 Adv. Differ. Eqs. 30 840386
[10]	Hilscher R Š and Zeidan V 2012 Nonlinear Anal. 75 932
[11]	Ferreira R A C and Torres D F M 2007 Math. Control Theory Fin. 136 145
[12]	Bohner M 2004 Dyn. Sys. Appl. 13 339
[13]	Martins N and Torres D F M 2009 Nonlinear Anal. 71 e763
[14]	Torres D F M 2010 Int. J. Sim. Mult. Des. Optim. 4 11
[15]	Bartosiewicz Z, Martins N and Torres D F M 2010 Eur. J. Control 17 9
[16]	Malinowska A B and Ammi M R S 2014 Int. J. Differ. Eqs. 9 87
[17]	Guo Z H and Gao P Y 1990 Acta Mech. Sin. 22 185(in Chinese)
[18]	Chen B 1991 Acta Mech. Sin. 23 379(in Chinese)
[19]	Guo Z H and Gao P Y 1992 Acta Mech. Sin. 24 253(in Chinese)
[20]	Cai P P, Fu J L and Guo Y X 2013 Sci. China G-Phys. Mech. Astron. 56 1017
[21]	Zu Q H and Zhu J Q 2016 J. Math. Phys. 57 082701
[22]	Song C J and Zhang Y 2015 J. Math. Phys. 56 102701
[23]	Jin S X and Zhang Y 2017 Chin. Phys. B 26 014501
[24]	Martins N and Torres D F M 2010 Appl. Math. Lett. 23 1432
[25]	Malinowska A B and Martins N 2013 Abstr. Appl. Anal. 2013 1728
[26]	Carlson D A 2015 J. Optim. Theory Appl. 166 351
[27]	Zhang Y 2016 Chin. Quar. Mech. 37 214(in Chinese)
[28]	Jin S X and Zhang Y 2017 Chin. Quar. Mech. 38 447(in Chinese)
[29]	Mei F X 2013 Analytical Mechanics (Beijing:Beijing Institute of Technology Press) (in Chinese)
[30]	Chen X W and Mei F X 2016 Mech. Res. Commun. 76 91
[31]	Guo H Y, Li Y Q, et al. 2002 Commun. Theor. Phys. 37 1
[32]	Mei F X, Liu D and Luo Y 1991 Advanced Analytical Mechanics (Beijing:Beijing Institute of Technology Press) (in Chinese)

Generalized Chaplygin equations for nonholonomic systems on time scales

Generalized Chaplygin equations for nonholonomic systems on time scales

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 32

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	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.
[2]	张冉, 彭淼, 张正娣, 毕勤胜. Bursting oscillations as well as the bifurcation mechanism in a non-smooth chaotic geomagnetic field model[J]. 中国物理B, 2018, 27(11): 110501-110501.
[3]	韩青爽, 陈帝伊, 张浩. Bursting oscillations in a hydro-turbine governing system with two time scales[J]. 中国物理B, 2017, 26(12): 128202-128202.
[4]	金世欣, 张毅. Methods of reduction for Lagrange systems on time scaleswith nabla derivatives[J]. 中国物理B, 2017, 26(1): 14501-014501.
[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]	孙毅, 陈本永, 傅景礼. Lie symmetry theorem of fractional nonholonomic systems[J]. , 2014, 23(11): 110201-110201.
[7]	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.
[8]	贾利群, 张美玲, 王肖肖, 韩月林 . Form invariance and approximate conserved quantity of Appell equations for a weakly nonholonomic system[J]. 中国物理B, 2012, 21(7): 70204-070204.
[9]	刘晓巍, 李元成. Lie–Mei symmetry and conserved quantities of the Rosenberg problem[J]. 中国物理B, 2011, 20(7): 70204-070204.
[10]	姜文安, 李状君, 罗绍凯. Mei symmetries and Mei conserved quantities for higher-order nonholonomic constraint systems[J]. 中国物理B, 2011, 20(3): 30202-030202.
[11]	刘畅, 常鹏, 刘世兴, 郭永新. Decomposition of almost-Poisson structure of generalised Chaplygin's nonholonomic systems[J]. 中国物理B, 2010, 19(3): 30302-030302.
[12]	吴惠彬, 梅凤翔. Symmetry of Lagrangians of nonholonomic systems of non-Chetaev's type[J]. 中国物理B, 2010, 19(3): 30303-030303.
[13]	周莎, 傅景礼, 刘咏松. Lagrange equations of nonholonomic systems with fractional derivatives[J]. 中国物理B, 2010, 19(12): 120301-120301.
[14]	庞婷, 方建会, 张明江, 蔺鹏, 路凯. A New type of conserved quantity deduced from Mei symmetry of nonholonomic systems in terms of quasi-coordinates[J]. 中国物理B, 2009, 18(8): 3150-3154.
[15]	解加芳, 冮铁强, 梅凤翔. Weak Noether symmetry for nonholonomic systems of non-Chetaev type[J]. 中国物理B, 2008, 17(9): 3175-3179.