The universal forms of the dynamic equations of holonomic mechanical system in relative motion

Zhang Xiang-Wu

doi:10.7498/aps.55.2669

Abstract
Based on the dynamic equations of particles system in non-inertial coordinate system, the higher order differential variational principle of relative motion for mechanical system is obtained, and the energy of higher order relative velocity of the mechanical system is introduced, the different kinds of higher order dynamic equations of holonomic mechanical system in relative motion are derived, and an example is given to illustrate the application of the results.

Keywords:
holonomic mechanical system /

relative motion /

higher order differential variational principle /

higher order dynamic equations
Authors and contacts
Zhang Xiang-Wu

1.
陇东学院物理系，庆阳 745000
References

Cited By

[1]	Zhang Fang, Zhang Yao-Yu, Xue Xi-Chang, Jia Li-Qun. Conformal invariance and conserved quantity of Mei symmetry for Appell equation in a holonomic system in relative motion. Acta Physica Sinica, 2015, 64(13): 134501. doi: 10.7498/aps.64.134501
[2]	Jia Li-Qun, Sun Xian-Ting, Zhang Mei-Ling, Zhang Yao-Yu, Han Yue-Lin. Generalized Hojman conserved quantity deduced from generalized Lie symmetry of Appell equations for a variable mass mechanical system in relative motion. Acta Physica Sinica, 2014, 63(1): 010201. doi: 10.7498/aps.63.010201
[3]	Wang Ting-Zhi, Sun Xian-Ting, Han Yue-Lin. Conformal invariance and conserved quantity of relative motion holonomic dynamical system in phase space. Acta Physica Sinica, 2014, 63(10): 104502. doi: 10.7498/aps.63.104502
[4]	Wang Ting-Zhi, Sun Xian-Ting, Han Yue-Lin. Conformal invariance and conserved quantity for a variable mass holonomic system in relative motion. Acta Physica Sinica, 2013, 62(23): 231101. doi: 10.7498/aps.62.231101
[5]	Wang Xiao-Xiao, Sun Xian-Ting, Zhang Mei-Ling, Xie Yin-Li, Jia Li-Qun. Noether symmetry and Noether conserved quantity of Nielsen equation in a dynamical system of the relative motion with nonholonomic constraint of Chetaev's type. Acta Physica Sinica, 2012, 61(6): 064501. doi: 10.7498/aps.61.064501
[6]	Wang Xiao-Xiao, Zhang Mei-Ling, Han Yue-Lin, Jia Li-Qun. Mei symmetry and Mei conserved quantity of Nielsen equation in a dynamical system of the relative motion with nonholonomic constraint of Chetaev's type. Acta Physica Sinica, 2012, 61(20): 200203. doi: 10.7498/aps.61.200203
[7]	Lou Zhi-Mei, Mei Feng-Xiang. A second order gradient representation of mechanics system. Acta Physica Sinica, 2012, 61(2): 024502. doi: 10.7498/aps.61.024502
[8]	Luo Shao-Kai, Jia Li-Qun, Xie Yin-Li. Mei conserved quantity deduced from Mei symmetry of Appell equation in a dynamical system of relative motion. Acta Physica Sinica, 2011, 60(4): 040201. doi: 10.7498/aps.60.040201
[9]	Xie Yin-Li, Jia Li-Qun, Yang Xin-Fang. Lie symmetry and Hojman conserved quantity of Nielsen equation in a dynamical system of the relative motion. Acta Physica Sinica, 2011, 60(3): 030201. doi: 10.7498/aps.60.030201
[10]	Zheng Shi-Wang, Xie Jia-Fang, Chen Xiang-Wei, Du Xue-Lian. Another kind of conserved quantity induced directly from Mei symmetry of Tzénoff equations for holonomic systems. Acta Physica Sinica, 2010, 59(8): 5209-5212. doi: 10.7498/aps.59.5209
[11]	Xia Li-Li, Li Yuan-Cheng, Wang Xian-Jun. Non-Noether conserved quantities for nonholonomic controllable mechanical systems with relativistic rotational variable mass. Acta Physica Sinica, 2009, 58(1): 28-33. doi: 10.7498/aps.58.28
[12]	Mei Feng-Xiang, Wu Hui-Bin. Lagrange symmetry for a dynamical system of relative motion. Acta Physica Sinica, 2009, 58(9): 5919-5922. doi: 10.7498/aps.58.5919
[13]	Xia Li-Li, Li Yuan-Cheng. Non-Noether conserved quantity for relativistic nonholonomic controllable mechanical system with variable mass. Acta Physica Sinica, 2008, 57(8): 4652-4656. doi: 10.7498/aps.57.4652
[14]	Zhang Yi. Differential variational principles of mechanical systems in the event space. Acta Physica Sinica, 2007, 56(2): 655-660. doi: 10.7498/aps.56.655
[15]	Zhang Xiang-Wu. Higher order differential equations of motion for holonomic mechanical system of variable mass. Acta Physica Sinica, 2006, 55(4): 1543-1547. doi: 10.7498/aps.55.1543
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[17]	Zhang Xiang-Wu. Higher-order differential equations of motion of a holonomic mechanical system. Acta Physica Sinica, 2005, 54(9): 3978-3982. doi: 10.7498/aps.54.3978
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[19]	QIAO YONG-FEN, ZHAO SHU-HONG. EQUATIONS OF MOTION OF VARIABLE MASS NONHOLONOMIC DYNAMICAL SYSTEMS IN POINCARé-CHETAEV VARIABLES. Acta Physica Sinica, 2001, 50(5): 805-810. doi: 10.7498/aps.50.805
[20]	FANG JIAN-HUI. RELATIVISTIC DYNAMIC EQUATION AND VARIATIONAL PRINCIPLE FOR ROTATIONAL VARIABLE MASS SYSTEM. Acta Physica Sinica, 2000, 49(6): 1028-1030. doi: 10.7498/aps.49.1028

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Vol. 55, Issue 6 - 2006-03-20

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The universal forms of the dynamic equations of holonomic mechanical system in relative motion

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The universal forms of the dynamic equations of holonomic mechanical system in relative motion

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