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Nonholonomic Multibody Dynamics
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Nonholonomic Multibody Dynamics Gerald Kielau1 and Peter Maißer1 | (1) | Institute of Mechatronics at, the Chemnitz University of Technology, Reichenhainer Str. 88, D-09126 Chemnitz, Germany |
Abstract The paper deals with the nonholonomic multibody system dynamics from apoint of view which is caused by some actual applications in high-tecareas like high-speed train technology or biomechanics of somedisciplines in high-performance sports. Obviously, looking at suchproblems, there are very close connections between classical analyticaldynamics, differential geometry and modern control theory. But theseconnections cannot be used to get new composed results in solvingcomplicated problems of multibody system dynamics because correspondingsoftware tools are not enough in tune with each other. This paper willgive some ideas for developing a unified basis for modeling, simulationand control of nonholonomic multibody systems. First, a derivative-free approach for generating Lagrangian motionequations of multibody systems with kinematical tree structure as wellas for constrained multibody systems is given. This has been done byusing differential-geometric concepts in a Riemannian space. Secondly,the well-known theorem of Frobenius is considered with respect to itsclassical interpretation by the so-called object of nonholonomy as wellas by its modern interpretation in the nonlinear control theory usingLie-brackets. The ideas are illustrated by the classical rollingcondition and edge condition on double-curved surfaces. Specialnumerical problems in simulation of multibody systems subject toadditional kinematic constraints are discussed. Finally threeapplications are given. nonholonomic multibody systems - Riemannian geometry - Lagrangian equations
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