This paper reviews the Euler–Rodrigues formula in the axis–angle representation of
rotations, studies its variations and derivations in different mathematical forms as vectors …

The compact classical Lie groups can be regarded as groups of n*n matrices over the real,
complex, and quaternion fields R,~C, and Q that satisfy metric-and volume-conserving …

Locomotion is a fundamental human skill. Real-time sensing and feedback is a promising
strategy for motion training to reconstruct healthy locomotion patterns lost due to aging or …

Synthesizing motion de novo for dynamic virtual organisms in a physics-based, virtual
environment is presently intractable. Multi-body simulation development within current …

Across computer graphics, vision, robotics and simulation, many applications rely on
determining the 3D rotation that aligns two objects or sets of points. The standard solution is …

In this paper, the problem of the decomposition of a rigid body displacement by a succession
of three rigid body displacements with specified screw-axis is completely solved. Using the …

Here we derive analytic expressions for the scalar parameters which appear in the
generalized Euler decomposition of the rotational matrices in R^3. The axes of rotations in …

In this article we suggest a new method, partially based on earlier works of Wohlhart 15,
Mladenova and Mladenov 11, Brezov et al 3, that resolves the generalized Euler …

Here we use an extension of Rodrigues' vector parameter construction for pseudo-rotations
in order to obtain explicit formulae for the generalized Euler decomposition with arbitrary …

In this article, a novel characterization of the workspace of 3R chains with non-orthogonal,
intersecting axes is derived by describing the set of singular orientations as two tori that …