Stability of Motion for a Constrained Birkhoff’s System in Terms of Independent Variables

Mei Fengxiang

Volume 18 Issue 1

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1997 > 18(1): 55-60

Mei Fengxiang. Stability of Motion for a Constrained Birkhoff’s System in Terms of Independent Variables[J]. Applied Mathematics and Mechanics, 1997, 18(1): 55-60.

Citation:

Mei Fengxiang. Stability of Motion for a Constrained Birkhoff’s System in Terms of Independent Variables[J]. Applied Mathematics and Mechanics, 1997, 18(1): 55-60.

Citation:

Mei Fengxiang. Stability of Motion for a Constrained Birkhoff’s System in Terms of Independent Variables[J]. Applied Mathematics and Mechanics, 1997, 18(1): 55-60.

PDF( 2461 KB)

Stability of Motion for a Constrained Birkhoff’s System in Terms of Independent Variables

Mei Fengxiang

Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, P. R. China

Received Date: 1995-10-16
Publish Date: 1997-01-15

Abstract

Abstract

This paper proposes firstly the pfaff-Birkhoff-D'Alembert's principle and obtains the equations of motion in terms of the independent variables for a constrained Birkhoff's system from the principle. Secondly, it establishes the equations of perturbation of the system. Finally, it obtains the stability criteria by using the Liaqpunov direct method and the firstly approximate method.
- dynamics,
- Birkhoff’s system,
- stability of motion

FullText(HTML)

References(10)

References

[1]	G. D. Birkhoff Dynamical Systems, AMS College Publ., Providence RI (1927), 89-91.
[2]	R. M. Santilli, Foundations of Theorencat Mechanics II Springer-Verlag, New York(1983), 30-40.
[3]	А.С.Галиуллин,Аналитинескаи динамика,Высшая Школа,Москва(1989),249-263.
[4]	梅凤翔、史荣昌,关于Pfaff-Birkhoff原理,北京理工大学学报,13 (2Ⅱ) (1993)256-273.
[5]	戴贤扬、赵关康、梅凤翔,Chaplygin非完整系统的Birkhoff表示,《中国非完整力学三十年》,河南大学出版社,开封(1994). 107-109.
[6]	梅凤翔,Birkhoff系统灼Noether理论,中国科学,A辑,23(7) (1993), 709-717.
[7]	梅凤翔,Birkhoff系统动力学逆问题,北京师范学院学报,4 (1992),32-36.
[8]	梅凤翔,Birkhoff自治系统的平衡稳定性,科学通报,38(4) (1993), 311-313.
[9]	Shi Rongchang, Mei Fengxiang and Zhu Haiping, On the stability of the motion of a Birkhoff system, Mechanics Research Communications, 21, 3 (1994), 269-272.
[10]	吴惠彬、梅凤翔,广义Birkhoff系统的变换理论,科学通报,40(10)(1995), 885-888.

Relative Articles

[1]	WU Feng, ZHONG Wanxie. A Note on Symplectic Water Wave Dynamics[J]. Applied Mathematics and Mechanics, 2019, 40(1): 1-7. doi: 10.21656/1000-0887.390254
[2]	ZHANG Yan, LI Fanru, LI Wei, LIU Zuojun. Dynamic Analysis and Simulation of the Lower Extremity Exoskeleton Based on Human-Machine Interaction[J]. Applied Mathematics and Mechanics, 2019, 40(7): 780-790. doi: 10.21656/1000-0887.390212
[3]	ZHONG Wanxie, WU Feng, SUN Yan, YAO Zheng. Symplectic Water Wave Dynamics[J]. Applied Mathematics and Mechanics, 2018, 39(8): 855-874. doi: 10.21656/1000-0887.390062
[4]	ZHU Ren-chuan, MIAO Guo-ping, FAN Ju, LIU Hua. Offshore Floating Wind Turbines and Related Dynamic Problems[J]. Applied Mathematics and Mechanics, 2013, 34(10): 1110-1118. doi: 10.3879/j.issn.1000-0887.2013.10.011
[5]	DING Xi-lun, DING Xi-lun. Screw Theoretic View on Dynamics of Spatially Compliant Beam[J]. Applied Mathematics and Mechanics, 2010, 31(9): 1118-1132. doi: 10.3879/j.issn.1000-0887.2010.09.011
[6]	ZHANG Ding-guo. Recursive Lagrangian Dynamic Modeling and Simulation of Multi-Link Spatial Flexible Manipulator Arms[J]. Applied Mathematics and Mechanics, 2009, 30(10): 1202-1212. doi: 10.3879/j.issn.1000-0887.2009.10.008
[7]	ZHANG Ding-guo, ZHOU Sheng-feng. Dynamic Analysis of Flexible-Link and Flexible-Joint Robots[J]. Applied Mathematics and Mechanics, 2006, 27(5): 615-623.
[8]	HUANG Wei-jiang, LUO En, SHE Hui. Unconventional Hamilton-Type Variational Principles For Dynamics of Reissner Sandwich Plate[J]. Applied Mathematics and Mechanics, 2006, 27(1): 67-74.
[9]	LUO Shao-kai. Form Invariance and Noether Symmetrical Conserved Quantity of Relativistic Birkhoffian Systems[J]. Applied Mathematics and Mechanics, 2003, 24(4): 414-422.
[10]	GUO Yong-xin, SHANG Mei, LUO Shao-kai. Poincaré-Cartan Integral Invariants of Birkhoffian Systems[J]. Applied Mathematics and Mechanics, 2003, 24(1): 62-66.
[11]	ZHANG Xing-wu, WU Ji-ke, ZHU Hai-ping, HUANG Ke-fu. Generalized Canonical Transformation and Symplectic Algorithm of the Autonomous Birkhoffian Systems[J]. Applied Mathematics and Mechanics, 2002, 23(9): 915-920.
[12]	HU Chao, WANG Yan, WANG Li-guo, HUANG Wen-hu. Application of Mechanized Mathematics to Rotor Dynamics[J]. Applied Mathematics and Mechanics, 2002, 23(9): 929-935.
[13]	XU Jian-guo, JIA Jun-guo. Study on Dynamics, Stability and Control of Multi-Body Flexible Structure System in Functional Space[J]. Applied Mathematics and Mechanics, 2001, 22(12): 1267-1277.
[14]	Zhang Dingguo. The Addendum for the Generalized d’Alembert Equations of Motion[J]. Applied Mathematics and Mechanics, 2000, (1): 67-72.
[15]	Zhang Dingguo. The Equations of External lmpacted Dynamics between Multi-Rigidbody Systems[J]. Applied Mathematics and Mechanics, 1997, 18(6): 551-555.
[16]	Wang Yibing, Zhao Weijia, Pan Zhenkuan. A New Algorithm for Solving Differential/Algehraic Equations of Multibody System Dynamics[J]. Applied Mathematics and Mechanics, 1997, 18(9): 845-852.
[17]	Zhang Dingguo. The Lagrange Dynamic Equations of Multi-Rigidhody Systems with External Shocks[J]. Applied Mathematics and Mechanics, 1996, 17(6): 563-568.
[18]	Zhang Dingguo. Computer Simulation of the Motion of the Bullet Belt of Airplane Gun[J]. Applied Mathematics and Mechanics, 1996, 17(11): 997-1004.
[19]	Shui Xiaoping, Zhang Yongfa. A Method for Solving the Dynamics of Multibody Systems With Rheonomic and Nonholonomic Constraints[J]. Applied Mathematics and Mechanics, 1996, 17(6): 551-557.
[20]	Xing Jing-tang, Zheng Zhao-chang. Some General Theorems and Generalized and Piecewise Generalized Variational Principles for Linear Elastodynamics[J]. Applied Mathematics and Mechanics, 1992, 13(9): 795-810.