Graph theoretic foundations of multibody dynamics

Jain, Abhinandan

doi:10.1007/s11044-011-9267-6

Cited by 20 publications

(17 citation statements)

References 14 publications

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“…Further, they demonstrated through an example the applicability of graph-theoretic methods to represent and generate the dynamic and sensitivity equations for a given system. Jain [23] used the concepts of graph theory to get a better understanding of the mathematical foundations of multibody dynamics. He shed light on the clarification of graph theoretic structural properties of spatial operator techniques in multibody dynamics In the end, he exploited these structural properties for developing a broad spectrum of analytical results and computational algorithms.…”

Section: Mechanical and Multibody Systemsmentioning

confidence: 99%

An Overview of the Main Topics and Applications of Graph Theoretic Problems in Multiphysics Engineering

Garziad¹,

Saka²

2017

J Appl Mech Eng

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Graph-theoretic concepts are mostly used to study different applications in various areas such as electrical and mechanical engineering, generally multi-physics systems. The interest of researchers on this theory has importantly increased in the last decade. The main goal of this paper is to provide an overview of the use and applications of graph theoretic concept in modelling and analysis of systems in different fields. Therefore, the research topics discussed in this review are going to respect all the mentioned domains and the countries that apply this theory formulation in addition to the community of researchers who are identified by their publishers.

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Section: Mechanical and Multibody Systemsmentioning

confidence: 99%

An Overview of the Main Topics and Applications of Graph Theoretic Problems in Multiphysics Engineering

Garziad¹,

Saka²

2017

J Appl Mech Eng

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“…This is the common starting point for various O (n) methods [60][61][62]80,81] . Thus, the basic operations are the same.…”

Section: Open Issuesmentioning

confidence: 99%

Geometric methods and formulations in computational multibody system dynamics

Müller

Terze

2016

Acta Mech

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Multibody systems are dynamical systems characterized by intrinsic symmetries and invariants. Geometric mechanics deals with the mathematical modeling of such systems and has proven to be a valuable tool providing insights into the dynamics of mechanical systems, from a theoretical as well as from a computational point of view. Modeling multibody systems, comprising rigid and flexible members, as dynamical systems on manifolds, and Lie groups in particular, leads to frame-invariant and computationally advantageous formulations. In the last decade, such formulations and corresponding algorithms are becoming increasingly used in various areas of computational dynamics providing the conceptual and computational framework for multibody, coupled, and multiphysics systems, and their nonlinear control. The geometric setting, furthermore, gives rise to geometric numerical integration schemes that are designed to preserve the intrinsic structure and invariants of dynamical systems. These naturally avoid the long-standing problem of parameterization singularities and also deliver the necessary accuracy as well as a long-term stability of numerical solutions. The current intensive research in these areas documents the relevance and potential for geometric methods in general and in particular for multibody system dynamics. This paper provides an exhaustive summary of the development in the last decade, and a panoramic overview of the current state of knowledge in the field.

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“…In particular, directions are often assigned so to form a root-directed spanning (Jain, 2011a;Wittenburg, 2008 …”

Section: Remarkmentioning

confidence: 99%

Representation of the kinematic topology of mechanisms for kinematic analysis

Müller

2015

Mech. Sci.

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Abstract. The kinematic modeling of multi-loop mechanisms requires a systematic representation of the kinematic topology, i.e. the arrangement of links and joints. A linear graph, called the topological graph, is used to this end. Various forms of this graph have been introduced for application in mechanism kinematics and multibody dynamics aiming at matrix formulations of the governing equations. For the (higher-order) kinematic analysis of mechanisms a simple yet stringent representation of the topological information is often sufficient. This paper proposes a simple concept and notation for use in kinematic analysis. Upon a topological graph, an order relation of links and joints is introduced allowing for recursive computation of the mechanism configuration. An ordering is also introduced on the topologically independent fundamental cycles. The latter is indispensable for formulating generically independent loop closure constraints. These are presented for linkages with only lower pairs, as well as for mechanisms with one higher kinematic pair per fundamental cycle. The corresponding formulation is known as cut-body and cut-joint approach, respectively.

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Graph theoretic foundations of multibody dynamics

Cited by 20 publications

References 14 publications

An Overview of the Main Topics and Applications of Graph Theoretic Problems in Multiphysics Engineering

An Overview of the Main Topics and Applications of Graph Theoretic Problems in Multiphysics Engineering

Geometric methods and formulations in computational multibody system dynamics

Representation of the kinematic topology of mechanisms for kinematic analysis

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