scholarly journals Rigid body dynamics in terms of quaternions: Hamiltonian formulation and conserving numerical integration

2009 ◽  
Vol 79 (4) ◽  
pp. 444-473 ◽  
Author(s):  
Peter Betsch ◽  
Ralf Siebert
Keyword(s):  
Rigid Body ◽  
Numerical Integration ◽  
Hamiltonian Formulation ◽  
Rigid Body Dynamics ◽  
Body Dynamics

scholarly journals Numerical integration of rigid body dynamics in terms of quaternions

PAMM ◽  
2008 ◽  
Vol 8 (1) ◽  
pp. 10139-10140 ◽  
Author(s):  
Ralf Siebert ◽  
Peter Betsch
Keyword(s):  
Rigid Body ◽  
Numerical Integration ◽  
Rigid Body Dynamics ◽  
Body Dynamics

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

2016 ◽  
Vol 83 (6) ◽  
Author(s):  
Xiaoming Xu ◽  
Wanxie Zhong
Keyword(s):  
Kinetic Energy ◽  
Rigid Body ◽  
Numerical Integration ◽  
Iterative Scheme ◽  
Rigid Body Dynamics ◽  
Numerical Error ◽  
Inertial Parameter ◽  
Integration Schemes ◽  
Principal Moments Of Inertia ◽  
Body Dynamics

Inertia plays a crucial role in the quaternion-based rigid body dynamics, the associated mass matrix, however, presents singularity in the traditional representation. Recent researches demonstrated that the singularity can be avoided by adding an extra term into kinetic energy via a multiplier. Here, we propose a modified inertia representation through splitting the kinetic energy into two parts, where a square term of quaternion velocity, governed by an extra inertial parameter, is separated from the original expression. We further derive new numerical integration schemes in both Lagrange and Hamilton framework. Error estimation shows that the extra inertial parameter has a significant influence on the numerical error in discretization, and an iterative scheme of optimizing the extra inertial parameter to reduce the numerical error in simulation is proposed for quaternion-based rigid body dynamics. Numerical results demonstrate that the mean value of the three principal moments of inertia is a reasonable value of the extra inertia parameter which can impressively improve the accuracy in most cases, and the iterative scheme can further reduce the numerical error for numerical integration, taking the implementation in Lagrange's frame as an example.

scholarly journals Slipping–rolling transitions of a body with two contact points

2021 ◽  
Author(s):  
Mate Antali ◽  
Gabor Stepan
Keyword(s):  
Rigid Body ◽  
Contact Point ◽  
Static Friction ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Friction Forces ◽  
Contact Points ◽  
Body Dynamics ◽  
Coulomb Model ◽  
Rigid Surfaces

AbstractIn this paper, the general kinematics and dynamics of a rigid body is analysed, which is in contact with two rigid surfaces in the presence of dry friction. Due to the rolling or slipping state at each contact point, four kinematic scenarios occur. In the two-point rolling case, the contact forces are undetermined; consequently, the condition of the static friction forces cannot be checked from the Coulomb model to decide whether two-point rolling is possible. However, this issue can be resolved within the scope of rigid body dynamics by analysing the nonsmooth vector field of the system at the possible transitions between slipping and rolling. Based on the concept of limit directions of codimension-2 discontinuities, a method is presented to determine the conditions when the two-point rolling is realizable without slipping.

New solutions of classical problems in rigid body dynamics

2015 ◽  
Vol 69 ◽  
pp. 40-44
Author(s):  
H.M. Yehia ◽  
E. Saleh ◽  
S.F. Megahid
Keyword(s):  
Rigid Body ◽  
Rigid Body Dynamics ◽  
Body Dynamics

scholarly journals In Silico Single-Molecule Manipulation of DNA with Rigid Body Dynamics

2014 ◽  
Vol 10 (2) ◽  
pp. e1003456 ◽  
Author(s):  
Pascal Carrivain ◽  
Maria Barbi ◽  
Jean-Marc Victor
Keyword(s):  
Rigid Body ◽  
Single Molecule ◽  
In Silico ◽  
Rigid Body Dynamics ◽  
Body Dynamics ◽  
Single Molecule Manipulation

On so‐called singular constraints in rigid‐body dynamics

1986 ◽  
Vol 54 (7) ◽  
pp. 585-586
Author(s):  
Stephen F. Felszeghy
Keyword(s):  
Rigid Body ◽  
Rigid Body Dynamics ◽  
Body Dynamics

Rigid Body Dynamics

2014 ◽  
pp. 191-227 ◽  
Author(s):  
Pål Johan From ◽  
Jan Tommy Gravdahl ◽  
Kristin Ytterstad Pettersen
Keyword(s):  
Rigid Body ◽  
Rigid Body Dynamics ◽  
Body Dynamics
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