基于高斯最小拘束原理的多体系统动力学分析
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摘要
从受理想约束的多体系统出发,以广义坐标表示系统中各刚体的矢径,由达朗伯原理推出以加速度为变量的多体系统拘束函数表达式。对于受非理想约束的多体系统,可将非理想约束力看作系统所受的主动力的一部分,得出非理想约束系统的拘束函数表达式。对高斯最小拘束函数表达式进行变形,运用最小二乘法推导系统真实加速度的表达式。最后运用该建模方法对平面双摆系统进行建模及仿真,得到其位移、速度变化规律。
Starting from the ideal constraint multi body system,generalized coordinates are used to represent the radius vector of the rigid body in the system. Multi body system restraint function expression is obtained by D'Alembert principle with acceleration as variables. For the multi body system with non ideal constraints,the non ideal constraint is considered as a part of the active force. Gauss' s minimal constraint function expression is deformed,then the least square method is used to get the expression of generalized acceleration. In the end,the modeling and simulation of the planar double pendulum system are carried out to get the law of displacement and velocity change.
Starting from the ideal constraint multi body system,generalized coordinates are used to represent the radius vector of the rigid body in the system. Multi body system restraint function expression is obtained by D'Alembert principle with acceleration as variables. For the multi body system with non ideal constraints,the non ideal constraint is considered as a part of the active force. Gauss' s minimal constraint function expression is deformed,then the least square method is used to get the expression of generalized acceleration. In the end,the modeling and simulation of the planar double pendulum system are carried out to get the law of displacement and velocity change.
引文
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[3]Kalaba R,Uatsuyama H,Udwadia F.An extension of Gauss’s principle of Le-ast constraint[J],Inter Journal of General Systems,2004,33(1):63-69.
[4]姚文莉,戴葆青.广义坐标形式的高斯最小拘束原理及其推广[J].力学与实践,2014,36(6):779-785.
[5]Udwadia F E,Kalaba R E.A new perspective on constrained motion[J],Proc R Soc A,1992,39(4):407-410.
[6]Bruyninckx H,Khatib O.Gauss principle and the dynamics of redundant and constrained manipulators[C]∥Proceedings of the 2000IEEE International Conference on Robotics&Automation,San Francisco,CA,U.S.A,2000:2563-2568.
[7]史跃东,王德石.多体系统动力学的高斯拘束分析方法[J].力学与实践,2010,32(6):23-26.
[8]史跃东,王德石.高斯最小拘束原理在火炮振动分析中的应用[J].火炮发射与控制学报,2009(4):26-30.
[9]董龙雷,闫桂荣,杜彦亭.高斯最小拘束原理在一类刚柔耦合系统分析中的应用[J].兵工学报,2001,22(3):347-351.
[10]郝名望,叶正寅.单柔体与多柔体动力学的高斯最小拘束原理[J].广西大学学报,2001,36(2):195-204.
[11]刘延柱.基于高斯原理的多体系统动力学建模[J].力学学报,2014(4):940-945.
[12]Kalaba R E.Udwadia F E.Equations of motion for nonholonomic[J].Constrained Dynamical Systems via Mechanics,1993,60:662-668.
[13]高珍珍.广义逆矩阵及其应用[J].伊犁师范学院学报,2011(4):1-7.
[14]李庆扬,王能超,易大义.数值分析[M].北京:清华大学出版社,2001:90-96.
[2]刘延柱.高等动力学[M].北京:高等教育出版社,2001:46-48.
[3]Kalaba R,Uatsuyama H,Udwadia F.An extension of Gauss’s principle of Le-ast constraint[J],Inter Journal of General Systems,2004,33(1):63-69.
[4]姚文莉,戴葆青.广义坐标形式的高斯最小拘束原理及其推广[J].力学与实践,2014,36(6):779-785.
[5]Udwadia F E,Kalaba R E.A new perspective on constrained motion[J],Proc R Soc A,1992,39(4):407-410.
[6]Bruyninckx H,Khatib O.Gauss principle and the dynamics of redundant and constrained manipulators[C]∥Proceedings of the 2000IEEE International Conference on Robotics&Automation,San Francisco,CA,U.S.A,2000:2563-2568.
[7]史跃东,王德石.多体系统动力学的高斯拘束分析方法[J].力学与实践,2010,32(6):23-26.
[8]史跃东,王德石.高斯最小拘束原理在火炮振动分析中的应用[J].火炮发射与控制学报,2009(4):26-30.
[9]董龙雷,闫桂荣,杜彦亭.高斯最小拘束原理在一类刚柔耦合系统分析中的应用[J].兵工学报,2001,22(3):347-351.
[10]郝名望,叶正寅.单柔体与多柔体动力学的高斯最小拘束原理[J].广西大学学报,2001,36(2):195-204.
[11]刘延柱.基于高斯原理的多体系统动力学建模[J].力学学报,2014(4):940-945.
[12]Kalaba R E.Udwadia F E.Equations of motion for nonholonomic[J].Constrained Dynamical Systems via Mechanics,1993,60:662-668.
[13]高珍珍.广义逆矩阵及其应用[J].伊犁师范学院学报,2011(4):1-7.
[14]李庆扬,王能超,易大义.数值分析[M].北京:清华大学出版社,2001:90-96.