Coordinate Mappings for Rigid Body Motions

[1]  E. Celledoni,et al.  Lie group methods for rigid body dynamics and time integration on manifolds , 2003 .

[2]  Andreas Müller,et al.  Lie-group integration method for constrained multibody systems in state space , 2011 .

[3]  W. Magnus On the exponential solution of differential equations for a linear operator , 1954 .

[4]  Gr Geert Veldkamp On the use of dual numbers, vectors and matrices in instantaneous, spatial kinematics , 1976 .

[5]  Daniel J. Rixen,et al.  Parametrization of finite rotations in computational dynamics: a review , 1995 .

[6]  J. Marsden,et al.  Introduction to mechanics and symmetry , 1994 .

[7]  John L. Crassidis,et al.  Geometric Integration of Quaternions , 2012 .

[8]  Moshe Shoham,et al.  Dual numbers representation of rigid body dynamics , 1999 .

[9]  Jonghoon Park,et al.  Geometric integration on Euclidean group with application to articulated multibody systems , 2005, IEEE Transactions on Robotics.

[10]  Z. Terze,et al.  An Angular Momentum and Energy Conserving Lie-Group Integration Scheme for Rigid Body Rotational Dynamics Originating From Störmer–Verlet Algorithm , 2015 .

[11]  S. Helgason Differential Geometry, Lie Groups, and Symmetric Spaces , 1978 .

[12]  Olivier A. Bauchau,et al.  The Vector Parameterization of Motion , 2003 .

[13]  Peter Betsch,et al.  Rigid body dynamics in terms of quaternions: Hamiltonian formulation and conserving numerical integration , 2009 .

[14]  Ahmed A. Shabana,et al.  Dynamics of Multibody Systems , 2020 .

[15]  Arne Marthinsen,et al.  Runge-Kutta Methods Adapted to Manifolds and Based on Rigid Frames , 1999 .

[16]  G. Darboux,et al.  Leçons sur la Théorie Générale des Surfaces et les Applications Géométriques Du Calcul Infinitésimal , 2001 .

[17]  D. Sattinger,et al.  Lie Groups and Algebras with Applications to Physics, Geometry and Mechanics , 1986 .

[18]  J. M. Selig Cayley maps for SE(3) , 2007 .

[19]  Manfred Husty,et al.  Algebraic Geometry and Kinematics , 2009 .

[20]  J. C. Simo,et al.  Unconditionally stable algorithms for rigid body dynamics that exactly preserve energy and momentum , 1991 .

[21]  D. Siminovitch Rotations in NMR: Part I. EulerRodrigues parameters and quaternions , 1997 .

[22]  O. Bauchau,et al.  The Vectorial Parameterization of Rotation , 2003 .

[23]  H. Munthe-Kaas High order Runge-Kutta methods on manifolds , 1999 .

[24]  J. M. Selig Geometric Fundamentals of Robotics , 2004, Monographs in Computer Science.

[25]  Z. Terze,et al.  Singularity-free time integration of rotational quaternions using non-redundant ordinary differential equations , 2016 .

[26]  Richard M. Murray,et al.  A Mathematical Introduction to Robotic Manipulation , 1994 .

[27]  A. Ibrahimbegovic,et al.  Computational aspects of vector-like parametrization of three-dimensional finite rotations , 1995 .

[28]  A. Iserles,et al.  Lie-group methods , 2000, Acta Numerica.

[29]  Andreas Müller,et al.  The significance of the configuration space Lie group for the constraint satisfaction in numerical time integration of multibody systems , 2014, ArXiv.

[30]  J. Michael McCarthy,et al.  Introduction to theoretical kinematics , 1990 .

[31]  Moshe Shoham,et al.  Application of Hyper-Dual Numbers to Multibody Kinematics , 2016 .

[32]  Olivier Bruls,et al.  Lie group generalized-α time integration of constrained flexible multibody systems , 2012 .

[33]  Satya N. Atluri,et al.  Variational approaches for dynamics and time-finite-elements: numerical studies , 1990 .

[34]  J. Junkins,et al.  Stereographic Orientation Parameters for Attitude Dynamics: A Generalization of the Rodrigues Parameters , 1996 .

[35]  S. Altmann Rotations, Quaternions, and Double Groups , 1986 .

[36]  A. Müller Erratum to: A note on the motion representation and configuration update in time stepping schemes for the constrained rigid body , 2016 .

[37]  Andreas Müller,et al.  Group Theoretical Approaches to Vector Parameterization of Rotations , 2010 .

[38]  J. Junkins,et al.  HIGHER-ORDER CAYLEY TRANSFORMS WITH APPLICATIONS TO ATTITUDE REPRESENTATIONS , 1997 .

[39]  Olivier A. Bauchau,et al.  Flexible multibody dynamics , 2010 .

[40]  Joseph Duffy,et al.  The principle of transference: History, statement and proof , 1993 .

[41]  Petr Krysl,et al.  Explicit Newmark/Verlet algorithm for time integration of the rotational dynamics of rigid bodies , 2005 .