关于非理想系统的伍德瓦迪亚-卡拉巴动力学方程的讨论
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摘要
讨论了由伍德瓦迪亚(Udwadia)和卡拉巴(Kalaba)提出的针对一般非理想系统的动力学方程,并对理想及非理想约束力的表达式进行了修改.修改后的表达式有更清晰的物理意义且显示了同物理定律相适应的理想约束力及非理想约束力之间的耦合效应.例子中分别采用经典的刚体动力学方法、伍德瓦迪亚-卡拉巴方法及修改后的伍德瓦迪亚-卡拉巴方法进行了对比研究,证实了对方程修改的意义.
The expressions for general non-ideal systems proposed by Udwadia--Kalaba are investigated and revised with regard to the forces of ideal constraints and non-ideal constraints. The new revised expressions have a clearer physical meaning and contain the coupling between the forces of ideal constraints and non-ideal constraints, as is consistent with the original physical law. An example by using three methods validates the results of this paper.
The expressions for general non-ideal systems proposed by Udwadia--Kalaba are investigated and revised with regard to the forces of ideal constraints and non-ideal constraints. The new revised expressions have a clearer physical meaning and contain the coupling between the forces of ideal constraints and non-ideal constraints, as is consistent with the original physical law. An example by using three methods validates the results of this paper.
引文
1 Udwadia FE,Kalaba RE.A new perspective on constrained motion.Proc R Soc A,1992,439:407-410
2 Udwadia FE,Kalaba RE.Analytical Dynamics:A New Approach.Cambridge:Cambridge University Press,1996
3 Udwadia FE.Fundamental principles of lagrangian dynamics:mechanical systems with non-ideal,holonomic,and non-holonomic constraints.J Math Anal Appl,2000,252:341-355
4 Udwadia FE,Kalaba RE.Non-ideal constraints and lagrangian dynamics.J Aerosp Eng,2000,13:17-22
5 Udwadia FE,Kalaba RE.Explicit equations of motion for systems with non-ideal constraints.ASME J Appl Mech,2001,68:462-467
6 Udwadia FE.New general principle of mechanics and its application to general nonideal nonholonomic systems.Journal of Engineering Mechanics,2005,131(4):443-450
7 Udwadia FE,Kalaba RE.What is the general form of the explicit equations of motion for mechanical systems?J Appl Mech,2002,39:335-339
8 Udwadia FE,Phohomsiri P.Explicit equations of motion for constrained mechanical systems with singular mass matrices and applications to multi-body dynamics.Proc R Soc A,2006,462:2097-2117
9 Udwadia FE,Phailaung Phohomsiri.Explicit Poincare’equations of motion for general constrained systems.Part I.Analytical results.Proc R Soc A,2007,463:1421-1434
10 Zhao H,Zhen SC,Chen YH.Dynamic modeling and simulation of multi-body systems using the Udwadia-Kalaba theory.Chinese Journal of Mechanical Engineering,2013,26(5):839-850
11 de Falco D,Pennestr E,Vita L.Multibody dynamics.In:Proc of Eccomas Thematic Conference,Madrid,Spain,2005
12 Ettore P,Valentini Pier P,de Domenico F.An application of the Udwadia–Kalaba dynamic formulation to flexible multibody systems.Journal of the Franklin Institute,2010,347(1):173-194
13 Cho H,Udwadia FE.Explicit solution to the full nonlinear problem for satellite formation-keeping.Acta Astronautica,2010,67:369-387
14 de Falco D,Pennestri E,Vita L.Investigation of the influence of pseudoinverse matrix calculations on multibody dynamics simulations by means of the Udwadia--Kalaba formulation.Journal of Aerospace Engineering,2009,22(4):365-372
15 Huang J,Chen YH,Zhong ZH.Udwadia-Kalaba approach for parallel manipulator dynamics.Journal of Dynamic Systems,Measurement,and Control,2013,135(6):1-11
16 Solomin JE,Zuccalli M.A geometric approach to the extended DAlembert principle of Dwadia-Kalaba-Hee-Chang.Quarterly of Applied Mathematics,2005,63(2):269-275
17 甄圣超,赵韩,黄康等.应用Udwadia-Kalaba理论对开普勒定律的研究.中国科学:物理学·力学·天文学,2014,44:24-31
2 Udwadia FE,Kalaba RE.Analytical Dynamics:A New Approach.Cambridge:Cambridge University Press,1996
3 Udwadia FE.Fundamental principles of lagrangian dynamics:mechanical systems with non-ideal,holonomic,and non-holonomic constraints.J Math Anal Appl,2000,252:341-355
4 Udwadia FE,Kalaba RE.Non-ideal constraints and lagrangian dynamics.J Aerosp Eng,2000,13:17-22
5 Udwadia FE,Kalaba RE.Explicit equations of motion for systems with non-ideal constraints.ASME J Appl Mech,2001,68:462-467
6 Udwadia FE.New general principle of mechanics and its application to general nonideal nonholonomic systems.Journal of Engineering Mechanics,2005,131(4):443-450
7 Udwadia FE,Kalaba RE.What is the general form of the explicit equations of motion for mechanical systems?J Appl Mech,2002,39:335-339
8 Udwadia FE,Phohomsiri P.Explicit equations of motion for constrained mechanical systems with singular mass matrices and applications to multi-body dynamics.Proc R Soc A,2006,462:2097-2117
9 Udwadia FE,Phailaung Phohomsiri.Explicit Poincare’equations of motion for general constrained systems.Part I.Analytical results.Proc R Soc A,2007,463:1421-1434
10 Zhao H,Zhen SC,Chen YH.Dynamic modeling and simulation of multi-body systems using the Udwadia-Kalaba theory.Chinese Journal of Mechanical Engineering,2013,26(5):839-850
11 de Falco D,Pennestr E,Vita L.Multibody dynamics.In:Proc of Eccomas Thematic Conference,Madrid,Spain,2005
12 Ettore P,Valentini Pier P,de Domenico F.An application of the Udwadia–Kalaba dynamic formulation to flexible multibody systems.Journal of the Franklin Institute,2010,347(1):173-194
13 Cho H,Udwadia FE.Explicit solution to the full nonlinear problem for satellite formation-keeping.Acta Astronautica,2010,67:369-387
14 de Falco D,Pennestri E,Vita L.Investigation of the influence of pseudoinverse matrix calculations on multibody dynamics simulations by means of the Udwadia--Kalaba formulation.Journal of Aerospace Engineering,2009,22(4):365-372
15 Huang J,Chen YH,Zhong ZH.Udwadia-Kalaba approach for parallel manipulator dynamics.Journal of Dynamic Systems,Measurement,and Control,2013,135(6):1-11
16 Solomin JE,Zuccalli M.A geometric approach to the extended DAlembert principle of Dwadia-Kalaba-Hee-Chang.Quarterly of Applied Mathematics,2005,63(2):269-275
17 甄圣超,赵韩,黄康等.应用Udwadia-Kalaba理论对开普勒定律的研究.中国科学:物理学·力学·天文学,2014,44:24-31