Conservative rigid body dynamics by convected base vectors with implicit constraints

Krenk, Steen; Nielsen, Martin Bjerre

doi:10.1016/j.cma.2013.10.028

Cited by 15 publications

(25 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…When applied to rigid body dynamics with a coordinate representation according to equation (19) the translational and rotational degrees of freedom (q t , q r ) may be separated according to the following theorem.…”

Section: The Equations Of Motionmentioning

confidence: 99%

Coordinate representations for rigid parts in multibody dynamics

Afzali-Far

Lidström

2016

Mathematics and Mechanics of Solids

View full text Add to dashboard Cite

The paper is concerned with coordinate representations for rigid parts in multibody dynamics. The discussion is based on the general theory of the dynamics of multibody systems under constraints. General configuration coordinates are introduced and the requirement of their regularity is discussed. The use of Euler angles, quaternions and linear coordinates, where quaternions and linear coordinates require constraint conditions, is analysed in detail. These coordinate systems are all shown to be regular. Equations of motion are formulated, using Lagrange's as well as Euler's equations, and they are supplemented by the appropriate constraint conditions in the cases of quaternions and linear coordinates. Mass matrices are derived, and in terms of the Euler angles the mass matrix components are products of trigonometric functions whereas in terms of quaternions the matrix components are quadratic polynomials. Using linear coordinates gives rise to a constant mass matrix. Thus, there is a decreasing degree of complexity, regarding mass matrix components, when going from Euler angles to linear coordinates. This is obtained at the expense of an increasing gross number of degrees of freedom and the necessary introduction of constraint conditions. The different equations of motion obtained are compared with respect to their structural complexity. In all representations the components of the angular velocity are explicitly calculated. This is not always the case in previous investigations of this subject. The paper also gives a new proof of the well-known relation between angular velocity and unit quaternions and their time derivative.

show abstract

Section: The Equations Of Motionmentioning

confidence: 99%

Coordinate representations for rigid parts in multibody dynamics

Afzali-Far

Lidström

2016

Mathematics and Mechanics of Solids

View full text Add to dashboard Cite

show abstract

“…The top is represented as a cone with dimensions equivalent to those used in [16][17][18]. As illustrated in Figure 2, the parameters are height .…”

Section: Regular Precessionmentioning

confidence: 99%

“…[1]. The initial conditions correspond to those used in [16][17][18] Recently, regular precession top is detailed discussed by Krenk and Nielsen, in their researches about energy-momentum conserving integrations of rigid body dynamics [17,18]. They observed that the numerical integrations are of significant nutation error in simulation of regular precession, whether the integrations are implemented in terms of unit quaternion or convected base vectors.…”

Section: Regular Precessionmentioning

confidence: 99%

On the Numerical Influences of Inertia Representation for Rigid Body Dynamics

Xu¹,

Zhong²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

View full text Add to dashboard Cite

show abstract

“…According to a formal definition of the index of DAEs [3], the early researches [4][5][6] underline that higher indices result in more arduous solving process, especially numerical difficulties associated with the solution of these index-3 DAEs. Due to these reasons, a large amount of effort [7][8][9][10][11][12][13][14][15][16][17][18] has been devoted to the study of computational methods in pseudovectors for handling the motion of rigid body.…”

Section: Introductionmentioning

confidence: 99%

On the Numerical Influences of Inertia Representation for Rigid Body Dynamics in Terms of Unit Quaternion

Zhong

2016

Journal of Applied Mechanics

View full text Add to dashboard Cite

Inertia plays a crucial role in rigid body dynamics, and the associated mass matrix is of various forms in representation. The influences of accuracy of different representation, however, have not drawn enough attention in previous researches about numerical simulation of rigid body dynamics. In the paper, the inertia representation is intensively investigated for rigid body dynamics and a modified formulation is derived through splitting the kinetic energy into two parts: a square term of velocity and a quadratic form in the derivatives with quadratic coefficients in generalized displacement, of which the proportion is controlled by a scaling parameter. Although the kinetic energy with different scaling parameters is theoretically equivalent in dynamics, error estimation demonstrates that accuracy of numerical scheme crucially depends on the particular value of scaling parameter if only rotational coordinates are expressed in pseudo vectors. This attractive feature distinguishes the modified formulation from others in numerical significance. According to the modified representation of inertia, a variational integrator is derived for rigid body dynamics in pseudo vectors. Numerical results demonstrate that the variational integrator, of which the scaling parameter is selected as the arithmetic mean of three principal moments of inertia tensor, is of impressively higher accuracy in simulation, especially compared with the integrations derived with the original formulation of mass matrix.

show abstract

Conservative rigid body dynamics by convected base vectors with implicit constraints

Cited by 15 publications

References 17 publications

Coordinate representations for rigid parts in multibody dynamics

Coordinate representations for rigid parts in multibody dynamics

On the Numerical Influences of Inertia Representation for Rigid Body Dynamics

On the Numerical Influences of Inertia Representation for Rigid Body Dynamics in Terms of Unit Quaternion

Contact Info

Product

Resources

About