Automatic integration of Euler-Lagrange equations with constraints

Gear, C. W.; Leimkuhler, Benedict; Gupta, Gopal

doi:10.1016/0377-0427(85)90008-1

Cited by 375 publications

(201 citation statements)

References 6 publications

Supporting

Mentioning

198

Contrasting

Unclassified

Order By: Relevance

“…5]. In the case of holonomic constraints, we can use the results on constrained Riccati equations given in [15], which readily apply to constrained multibody equations in the Gear-Gupta-Leimkuhler formulation [14].…”

Section: Riccati Approachmentioning

confidence: 99%

Simulation of multibody systems with servo constraints through optimal control

Altmann

Heiland

2016

Multibody Syst Dyn

View full text Add to dashboard Cite

We consider mechanical systems where the dynamics are partially constrained to prescribed trajectories. An example for such a system is a building crane with a load and the requirement that the load moves on a certain path.Enforcing this condition directly in form of a servo constraint leads to differentialalgebraic equations (DAEs) of arbitrarily high index. Typically, the model equations are of index 5, which already poses high regularity conditions. If we relax the servo constraints and consider the system from an optimal control point of view, the strong regularity conditions vanish, and the solution can be obtained by standard techniques.By means of the well-known n-car example and an overhead crane, the theoretical and expected numerical difficulties of the direct DAE and the alternative modeling approach are illustrated. We show how the formulation of the problem in an optimal control context works and address the solvability of the optimal control system. We discuss that the problematic DAE behavior is still inherent in the optimal control system and show how its evidences depend on the regularization parameters of the optimization.

show abstract

Section: Riccati Approachmentioning

confidence: 99%

Simulation of multibody systems with servo constraints through optimal control

Altmann

Heiland

2016

Multibody Syst Dyn

View full text Add to dashboard Cite

show abstract

“…Baumgarte stabilization [4] and the Augmented Lagrangian formulation [5] are among the numerous stabilization methods available for index-1 formulations. A stabilized formulation also exists for index-2 DAEs [8].…”

Section: Approaches To the Formulation And Simulation Of Systems Subjmentioning

confidence: 99%

On-Line Symbolic Constraint Embedding for Simulation of Hybrid Dynamical Systems

et al. 2005

View full text Add to dashboard Cite

Abstract. In this paper we present a simulator designed to handle multibody systems with changing constraints, wherein the equations of motion for each of its constraint configurations are formulated in minimal ODE form with constraints embedded before they are passed to an ODE solver. The constraint-embedded equations are formulated symbolically according to a re-combination of terms of the unconstrained equations, and this symbolic process is undertaken on-line by the simulator.Constraint-embedding undertaken on-the-fly enables the simulation of systems with an ODE solver for which constraints are not known prior to simulation start or for which the enumeration of all constraint conditions would be unwieldy because of their complexity or number. Issues of drift associated with DAE solvers that usually require stabilization are sidestepped with the constraint-embedding approach. We apply nomenclature developed for hybrid dynamical systems to describe the system with changing constraints and to distinguish the roles of the forward dynamics solver, a collision detector, and an impact resolver. We have developed a MATLAB r toolbox for symbolically generating equations of motion using Kane's method and prototyped a simulator with on-line constraint embedding and demonstrated the design in three representative examples.

show abstract

“…The system (1) is supposed to be of index 3 (in the sense of either Gear, Leimkuhler, & Gupta (1985) or of Hairer, Lubich, & Roche (1989)), i.e.…”

Section: Description Of the Problems To Be Studiedmentioning

confidence: 99%

“…For more details the interested reader is referred to Hairer, Lubich, & Roche (1989) and the literature cited there (e.g. Gear, Leimkuhler, & Gupta (1985) or Gear & Petzold (1984)). …”

Section: Description Of the Problems To Be Studiedmentioning

confidence: 99%