Abstract
The use of multi-bond graphs (MBGs) has an increasing importance in the development of large mechanical systems, called multi-body systems (MBS), composed of a finite number of rigid bodies interconnected by kinematical constraints. The constitutive relationships of multi-bond resistors, transformers, and gyrators give way to zero-order causal paths (ZCPs) whose most important peculiarity is that their associated topological loops involve more than one direction. Two different methods are used to solve the ZCPs. With the first one, Lagrange multipliers are introduced by means of new flows and efforts as break variables of causal paths, adding constraint equations. With the second one, break variables are used directly to open the ZCPs. The procedure used solves the problem and implies the presence of new variables and constraint equations. Several algorithms have been developed to obtain the set of equations. The result is a set of differential–algebraic equations (DAEs) solved using a backward differential formulae (BDF) numerical method. An application to multi-body systems with a combination of classes of ZCPs will be shown.
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Felez, J., Romero, G., Maroto, J., Martinez, M.L. (2011). Simulation of Multi-body Systems Using Multi-bond Graphs. In: Borutzky, W. (eds) Bond Graph Modelling of Engineering Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9368-7_9
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DOI: https://doi.org/10.1007/978-1-4419-9368-7_9
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