On the Error Control for Multistep Methods Applied to ODEs with Invariants and DAEs in Multibody Dynamics∗

Eich, Edda; Führer, Claus; Yen, Jeng

doi:10.1080/08905459508905233

Cited by 6 publications

(2 citation statements)

References 8 publications

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“…Numerical methods for rigid-body dynamics without friction or impact have been studied extensively in the engineering and also mathematics literature. See, for example, [34,143,124,122,52,2,123,111,33,107,46,42,142,13], in reverse chronological order. One of the reasons for this is the need to simulate mechanical systems, especially the complex mechanical systems that arise in manufacturing processes and robotics.…”

Section: Methodsmentioning

confidence: 99%

Rigid-Body Dynamics with Friction and Impact

2000

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Rigid-body dynamics with unilateral contact is a good approximation for a wide range of everyday phenomena, from the operation of car brakes to walking to rock slides. It is also of vital importance for simulating robots, virtual reality, and realistic animation. However, correctly modeling rigid-body dynamics with friction is difficult due to a number of discontinuities in the behavior of rigid bodies and the discontinuities inherent in the Coulomb friction law. This is particularly crucial for handling situations with large coefficients of friction, which can result in paradoxical results known at least since Painlevé [C. R. Acad. Sci. Paris, 121 (1895), pp. 112-115]. This single example has been a counterexample and cause of controversy ever since, and only recently have there been rigorous mathematical results that show the existence of solutions to his example. The new mathematical developments in rigid-body dynamics have come from several sources: "sweeping processes" and the measure differential inclusions of Moreau in the 1970s and 1980s, the variational inequality approaches of Duvaut and J.-L. Lions in the 1970s, and the use of complementarity problems to formulate frictional contact problems by Lötstedt in the early 1980s. However, it wasn't until much more recently that these tools were finally able to produce rigorous results about rigid-body dynamics with Coulomb friction and impulses.

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Section: Methodsmentioning

confidence: 99%

Rigid-Body Dynamics with Friction and Impact

2000

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“…The governing equations of constrained multibody system are a set of differential-algebraic equations (DAEs) of index three [1]. The DAEs are much different from the ordinary differential equations (ODEs) and the numerical integration of DAEs is dif®cult because of the violations in constraint equations.…”

Section: Introductionmentioning

confidence: 99%

A direct violation correction method in numerical simulation of constrained multibody systems

Chen

2000

Computational Mechanics

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A new direct violation correction method for constrained multibody systems is presented. It can correct the value of state variables of the systems directly so as to satisfy the constraint equations of motion. During the integration of the dynamic equations of constrained multibody systems, this method can ef®ciently control the violations of constraint equations within any given accuracy at each time-step. Compared to conventional indirect methods, especially Baumgarte's Constraint Violation Stabilization Method, this method has clear physical meaning, less calculation and obvious correction effect. Besides, this method has minor effect on the form of the dynamic equations of systems, so it is stable and highly accurate. A numerical example is provided to demonstrate the effectiveness of this method.

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A local-global stepsize control for multistep methods applied to semi-explicit index 1 differential-algebraic equations

Kulikov

Shindin

1999

Korean J. Comput. & Appl. Math.

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On the Error Control for Multistep Methods Applied to ODEs with Invariants and DAEs in Multibody Dynamics∗

Cited by 6 publications

References 8 publications

Rigid-Body Dynamics with Friction and Impact

Rigid-Body Dynamics with Friction and Impact

A direct violation correction method in numerical simulation of constrained multibody systems

A local-global stepsize control for multistep methods applied to semi-explicit index 1 differential-algebraic equations

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