广义坐标形式的高斯最小拘束原理及其推广
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摘要
当采用广义坐标描述系统的运动时,相比质点形式的高斯最小拘束原理,通过广义坐标形式的高斯最小拘束原理来建立动力学优化模型,计算效率更高.从高斯原理的变分形式出发推导了广义坐标形式的高斯最小拘束原理,并研究了非理想约束、单边约束及刚体碰撞情形下的高斯最小拘束原理的形式.研究认为:对刚体碰撞情形下,高斯最小拘束原理不能取代碰撞恢复定律,碰撞恢复定律以碰撞后广义速度的约束方程形式起作用.
When the generalized coordinates are used to describe the motion of a system,a higher computational efficiency will be achieved in using the Gauss principle of least constraint,as compared with in the form of mass points.Based on the Gauss principle in the form of variation,the Gauss principle of least constraint in generalized coordinates is derived.The principle is generalized to cases of non-ideal constraints,unilateral constraints and the collision of rigid body systems.For the collision problem of rigid body systems,it is shown that the collision law cannot be replaced by the Gauss principle of least constraint and it should be used in the form of constraint equations for generalized velocities after collision.
When the generalized coordinates are used to describe the motion of a system,a higher computational efficiency will be achieved in using the Gauss principle of least constraint,as compared with in the form of mass points.Based on the Gauss principle in the form of variation,the Gauss principle of least constraint in generalized coordinates is derived.The principle is generalized to cases of non-ideal constraints,unilateral constraints and the collision of rigid body systems.For the collision problem of rigid body systems,it is shown that the collision law cannot be replaced by the Gauss principle of least constraint and it should be used in the form of constraint equations for generalized velocities after collision.
引文
1陈滨.分析动力学(第2版).北京:北京大学出版社,2012
2梅风翔,刘端,罗勇.高等分析力学.北京:北京理工大学出版社,1991
3刘延柱.高等动力学.北京:高等教育出版社,2000
4黄昭度,钟奉俄.工程系统分析力学.北京:高等教育出版社,1992
5袁士杰,吕哲勤.多刚体系统动力学.北京:北京理工大学出版社,1991
6 Kalaba RE,Udwadia FE.Equations of motion for nonholonomic,constrained dynamical systems via Gauss's Principle.J Appl Mech,1993,60(3):662-668
7 Udwadia FE,Kalaba RE.A new perspective on constrained motion.Proc R Soc A,1992,439:407-410
2梅风翔,刘端,罗勇.高等分析力学.北京:北京理工大学出版社,1991
3刘延柱.高等动力学.北京:高等教育出版社,2000
4黄昭度,钟奉俄.工程系统分析力学.北京:高等教育出版社,1992
5袁士杰,吕哲勤.多刚体系统动力学.北京:北京理工大学出版社,1991
6 Kalaba RE,Udwadia FE.Equations of motion for nonholonomic,constrained dynamical systems via Gauss's Principle.J Appl Mech,1993,60(3):662-668
7 Udwadia FE,Kalaba RE.A new perspective on constrained motion.Proc R Soc A,1992,439:407-410