关于刚体系统的单侧约束运动
On Unilaterally Constrained Motions of Rigid Bodies Systems
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摘要: 本文研究了一大类刚体系统的单侧约束运动的局部和整体性质。主要结论是;局部地,这类系统的运动相当于某带过黎曼流形上的质点的运动;整体地,在能量守恒的假定下。这类系统相当于某带边黎曼流形上的台球系统。Abstract: In this paper, the unilaterally constrained motions of a large class of rigid bodies systems are studied both locally and globally. The main conclusion is that locally,such a system bahaves like a particle in a Riemannian manifold with boundary, globally, under the assumption of energy conservation, the system behaves like a billiards system over a Riemannina manifold with boundary.
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[1] J.J.Moreau,Quadratic programming in mechanics: dynamics of one-sided constraints,J.SIAM Control,4,1 (1996). [2] R.Abraham and J.E.Marsden,Foundations of Mechanics,2nd Edition,Addison-Wesley,Reading Mass (1978). [3] V.I.Arnold,Mathematical Methods in Classical Mechanics,Springer-Verlag (1978). [4] Ya G.Sinai,Introduction to Ergodic Theory,Princeton N.J.,Princeton Univ.Press(1976). [5] 李洪波,力学系统单侧约束的几何理论,北京大学硕士研究生毕业论文(1991). -
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