Differential‐Algebraic Equations in Riemannian Spaces and Applications to Multibody System Dynamics

Jungnickel, Uwe

doi:10.1002/zamm.19940740914

Cited by 13 publications

(7 citation statements)

References 11 publications

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“…It can be integrated in time to obtain kinetic motion of the system as well as constraint reactions. Although constraints at the acceleration level will be immanently satisfied since (15) is included in mathematical model (13) and will be explicitly solved during integration, the numerical non-stability of (15) can induce constraints violation at the both position and velocity level [9].…”

Section: Rghov Zlwk Lqkhuhqw Frqvwudlqw Ylrodwlrq Sureohpmentioning

confidence: 99%

“…If additional nh non-holonomic constraints (9), which are imposed on the system (beside h holonomic constraints (3) that define configuration manifold …”

Section: Non-holonomic Constraintsmentioning

confidence: 99%

“…Generally, in the case of non-holonomic systems, a separate partitioning procedure is necessary for stabilization at configuration and velocity level. This is specially true if the imposed non-holonomic constraints (9) can not be put in Pfaffian form. If nonholonomic constraints are non-linear in velocities (this kind of constraints can appear as a result of certain controlling actions), it will be necessary to determine a completely new correction gradient…”

Section: Non-holonomic Constraintsmentioning

confidence: 99%

“…If, beside holonomic constrains, the additional nonholonomic constraints given in Pfaffian form (10) are imposed on the system, the procedures [9,11], similar to those described above, allow for shaping of mathematical models given by (13), (17), (18).…”

mentioning

confidence: 99%

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Constraint Gradient Projective Method for Stabilized Dynamic Simulation of Constrained Multibody Systems

Terze

Naudet

Lefeber

2003

Volume 5: 19th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C

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Constraint gradient projective method for stabilization of constraint violation during integration of constrained multibody systems is in the focus of the paper. Different mathematical models for constrained MBS dynamic simulation on manifolds are surveyed and violation of kinematical constraints is discussed. As an extension of the previous work focused on the integration procedures of the holonomic systems, the constraint gradient projective method for generally constrained mechanical systems is discussed. By adopting differentialgeometric point of view, the geometric and stabilization issues of the method are addressed. It is shown that the method can be applied for stabilization of holonomic and non-holonomic constraints in Pfaffian and general form.

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Section: Rghov Zlwk Lqkhuhqw Frqvwudlqw Ylrodwlrq Sureohpmentioning

confidence: 99%

“…If additional nh non-holonomic constraints (9), which are imposed on the system (beside h holonomic constraints (3) that define configuration manifold …”

Section: Non-holonomic Constraintsmentioning

confidence: 99%

Section: Non-holonomic Constraintsmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Constraint Gradient Projective Method for Stabilized Dynamic Simulation of Constrained Multibody Systems

Terze

Naudet

Lefeber

2003

Volume 5: 19th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C

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“…'The geometric point of view in mechanics combined with solid analysis has been a phenomenal success in linking various lines' [1] (see also references [2][3][4][5]). Considering this dualism, even the multi-body system (MBS) dynamics is stimulated; see references [6][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Multi-body dynamics and electromechanics: From a differential-geometric point of view

Maißer

2005

Proceedings of the Institution of Mechanical Engineers, Part K:

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Mechanics is the origin of physics. Almost any physical theory like electrodynamics stems from mechanical explanations. The mathematical-geometric considerations in mechanics serve as a prototype for other physical theories. Consequently, developments in modern physics in turn have a feedback to mechanics in terms of its representation. The laws of nature can be expressed as differential equations. The fact that these equations can be solved by average computers has led most engineers and many mathematical physicists to neglect geometrical aspects for solving and better understanding their problems. The intimate relation between geometry and analysis led to the differential geometry, which is a valuable tool for a better understanding in many physical disciplines like classical mechanics, electrodynamics, and nowadays in mechatronics. It has been the development of the theory of relativity that revealed the paramount importance of the differential geometry. Many problems in research and development can be studied by differential-geometric methods. Modern non-linear control theories, for instance, are entirely based on the differential geometry. This paper addresses some aspects in mathematical modelling of multi-body and electromechanical systems. The motivation for this research arises from applications of linear induction machines in modern transport technologies.

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Differential-Geometric Aspects of Constrained System Dynamics

Blajer

2009

Advanced Design of Mechanical Systems: From Analysis to Optimization

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Differential‐Algebraic Equations in Riemannian Spaces and Applications to Multibody System Dynamics

Cited by 13 publications

References 11 publications

Constraint Gradient Projective Method for Stabilized Dynamic Simulation of Constrained Multibody Systems

Constraint Gradient Projective Method for Stabilized Dynamic Simulation of Constrained Multibody Systems

Multi-body dynamics and electromechanics: From a differential-geometric point of view

Differential-Geometric Aspects of Constrained System Dynamics

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