Convergence of a Time-Stepping Scheme for Rigid-Body Dynamics and Resolution of Painlevé's Problem

Stewart, David E.

doi:10.1007/s002050050129

Cited by 142 publications

(171 citation statements)

References 31 publications

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“…Together with the switch control (19) which can be stated with the help of u R = −R -3 from Equations (27), (21) as…”

Section: The Extended Dc-dc Buck Convertermentioning

confidence: 99%

“…Time-stepping methods are di erence schemes including fully the complementarity conditions and the impact laws, by allowing a simultaneous treatment of impulsive and non-impulsive forces together with all inequalities involved. More advanced discretization schemes may be found in the literature, such as the powerful -method in Reference [22], an algorithm based on displacements with proven convergence [23,24], or several other welldeveloped codes described in References [25][26][27].…”

Section: The Extended Dc-dc Buck Convertermentioning

confidence: 99%

“…With u R = −R-R from Equation (27), -R = -L − -C from the mesh transformation (21), and -L − -C = (1=RC)g C according to the second equation in Equation (54), one obtains u R = (−1=C)g C and therefore for the switch control (19) dA(g C ; t) = 0 if g C 6 Ch(t)…”

Section: The Original Dc-dc Buck Convertermentioning

confidence: 99%

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Models of non-smooth switches in electrical systems

Glocker

2005

Int. J. Circ. Theor. Appl.

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SUMMARYIdealized modelling of diodes, relays and switches in the framework of linear complementarity is introduced. Within the charge approach, the classical electromechanical analogy is extended to passively and actively switching components in electrical circuits. The associated branch relations are expressed in terms of set-valued functions, which allow to formulate the circuit's dynamic behaviour as a di erential inclusion. This approach is demonstrated by the example of the DC-DC buck converter. A di erence scheme, known in mechanics as time stepping, is applied for numerical approximation of the evolution problem. The discretized inclusions are formulated as a linear complementarity problem in standard form, which implicitly takes care of all switching events by its solution. State reduction, which requires manipulation of the set-valued branch relations in order to obtain a minimal model, is performed on the example of the buck converter.

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“…Together with the switch control (19) which can be stated with the help of u R = −R -3 from Equations (27), (21) as…”

Section: The Extended Dc-dc Buck Convertermentioning

confidence: 99%

Section: The Extended Dc-dc Buck Convertermentioning

confidence: 99%

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Models of non-smooth switches in electrical systems

Glocker

2005

Int. J. Circ. Theor. Appl.

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“…0 [15,19]. Moreover, the differential inclusion can be solved in terms of vector measures: forces can be impulsive and velocities can have discontinuities, thus supporting also the case of impacts and giving a weak solution to otherwise unsolvable situations like in the Painlevé paradox [20].…”

Section: The Formulation Of the Equations Of Motionmentioning

confidence: 94%

GPU-Based Parallel Computing for the Simulation of Complex Multibody Systems with Unilateral and Bilateral Constraints: An Overview

Tasora

Negrut²,

Anitescu

2010

Computational Methods in Applied Sciences

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This work reports on advances in large-scale multibody dynamics simulation facilitated by the use of the Graphics Processing Unit (GPU). A description of the GPU execution model along with its memory spaces is provided to illustrate its potential parallel scientific computing. The equations of motion associated with the dynamics of large system of rigid bodies are introduced and a solution method is presented. The solution method is designed to map well on the parallel hardware, which is demonstrated by an order of magnitude reductions in simulation time for large systems that concern the dynamics of granular material. One of the salient attributes of the solution method is its linear scaling with the dimension of the problem. This is due to efficient algorithms that handle in linear time both the collision detection and the solution of the nonlinear complementarity problem associated with the proposed approach. The current implementation supports the simulation of systems with more than one million bodies on commodity desktops. Efforts are under way to extend this number to hundreds of millions of bodies on small affordable clusters.

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“…For certain parameter and state combinations, it is impossible to find any consistent set of finite forces and accelerations and one needs to seek impulsive solutions for the unknown quantities. This problem and its variations stimulated a large body of work in frictional collisions [2,16,17,19], which hypothesize that the rigid rod would "jam" in such cases and start pivoting around its toe.…”

Section: Existence Of Solutions and Leg Jammingmentioning

confidence: 99%

Multi-Point Contact Models for Dynamic Self-Righting of a Hexapod

Saranlı¹,

Koditschek²

2005

Springer Tracts in Advanced Robotics

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Summary. In this paper, we report on the design of a model-based controller that can achieve dynamical self-righting of a hexapod robot. Extending on our earlier work in this domain, we introduce a tractable multi-point contact model with Coulomb friction. We contrast the singularities inherent to the new model with other available methods and show that for our specific application, it yields dynamics which are well-defined. We then present a feedback controller that achieves "maximal" performance under morphological and actuation constraints, while ensuring the validity of the model by staying away from singularities. Finally, through systematic experiments, we demonstrate that our controller is capable of robust flipping behavior.

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Convergence of a Time-Stepping Scheme for Rigid-Body Dynamics and Resolution of Painlevé's Problem

Cited by 142 publications

References 31 publications

Models of non-smooth switches in electrical systems

Models of non-smooth switches in electrical systems

GPU-Based Parallel Computing for the Simulation of Complex Multibody Systems with Unilateral and Bilateral Constraints: An Overview

Multi-Point Contact Models for Dynamic Self-Righting of a Hexapod

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