Dynamik und Regelung mechanischer Systeme

Bremer, Hartmut

doi:10.1007/978-3-663-05674-4

Cited by 104 publications

(41 citation statements)

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“…1. For more background on the principle of virtual work, the reader is referred to [4,5,7,17]. The force distribution dF in classical dynamics is composed of the constraint forces dF z and some remaining forces dF q , i.e.,…”

Section: Principle Of Virtual Workmentioning

confidence: 99%

Rigid body dynamics with a scalable body, quaternions and perfect constraints

Möller

Glocker

2011

Multibody Syst Dyn

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In this paper, we present a formulation of the quaternion constraint for rigid body rotations in the form of a standard perfect bilateral mechanical constraint, for which the associated Lagrangian multiplier has the meaning of a constraint force. First, the equations of motion of a scalable body are derived. A scalable body has three translational, three rotational, and one uniform scaling degree of freedom. As generalized coordinates, an unconstrained quaternion and a displacement vector are used. To the scalable body, a perfect bilateral constraint is added, restricting the quaternion to unit length and making the body rigid. This way a quaternion based differential algebraic equation (DAE) formulation for the dynamics of a rigid body is obtained, where the 7 × 7 mass matrix is regular and the unit length restriction of the quaternion is enforced by a mechanical constraint. Finally, the equations of motion in the form of a DAE are linked to the Newton-Euler equations of motion of a rigid body. The rigid body DAE formulation is useful for the construction of (energy) consistent integrators.

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Section: Principle Of Virtual Workmentioning

confidence: 99%

Rigid body dynamics with a scalable body, quaternions and perfect constraints

Möller

Glocker

2011

Multibody Syst Dyn

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“…Many books deal with the modeling of hybrid multibody systems [8,9,60]. Some publications examine especially the modeling and dynamics of elastic rotor systems [3,13,65,71].…”

Section: Elastic Rotormentioning

confidence: 99%

“…The superposed parts of the translational and the angular velocities can always be expressed as a linear combination of the minimal velocities (see [8]):…”

Section: Minimal Coordinates and Minimal Velocitiesmentioning

confidence: 99%

Control of a rubbing rotor using an active auxiliary bearing

Ginzinger

Ulbrich

2007

J Mech Sci Technol

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“…besonders strukturiert bestimmen, siehe [1]. M n , G n , Q n sind die entsprechenden Systemmatrizen des Subsystems, welchë uber die beschreibenden Geschwindigkeitenẏ n in die Minimaldarstellung projiziert werden.…”

Section: Modellbildungunclassified