How One Can Arrange the Multibody System Dynamics Computer Model

Abstract

The symplest computer models for mechanical systems can be organized using Cauchy normal form. Further complicating the mechanical model is able to bring us to application the implicit functions of next complexity level. Process of the multibody system computer models development is of special difficulty. There exist different ways for organizing such a models. Mainly these ways are reduced to the model transformation to the form of differential-algebraic equations (DAEs). These latter ones correspond to Lagrange equations of the first kind. Note that usually differential equations of DAEs mentioned correspond to dynamical and kinematical equations of mechanics, while the algebraic equations are generated by constraints. Computational experience makes it possible to classify objects of the multibody system dynamics [1]. Such a model includes two classes of objects. They correspond to notions of 'body' and 'constraint'. Let us also remark that these two classes of objects define the structure of the undirected graph such that 'bodies' play a role of the graph vertices, while 'constraints' play the role of edges. There exists yet another graph interpretation using the bi-chromatic bipartite graph. In this case both bodies and constraints are interpreted as vertices. Objects of bodies compose a partition and are coloured by one colour while objects of constraints compose the complement partition of the whole graph and are coloured by another colour. Edges connecting vertices of partitions for the graph are arranged in a way such that for any vertex of constraint there exist exactly two vertices of class 'body' thus implementing participation in the constraint. Two ways for the multibody system dynamics computer model graph composition mentioned above define ways for constructing the visual model of such a system thus defining ports interconnection structure. Different cases of the multibody system dynamics computer model implementation were analysed as an examples. Models under construction are the following ones: (a) Rattleback; (b) Snakeboard; (c) Skateboard; (d) Tippe-Top; (e) Ball Bearing; (f) Spur Involute Gear; (g) Omni­Vehicle.

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