Different MBS algorithms, however, employ different sets of orientation coordinates, such as Euler angles and Euler parameters, which lead to different forms of the dynamic equations of motion.
The nonlinear equations of motion of the gyroscope are formulated using two different sets of orientation parameters: Euler angles and Euler parameters.
In order to demonstrate the significant differences between the eigenvalue solutions associated with two different sets of orientation parameters, a simple rotating disk example is considered in this study.
As shown in this investigation, the frequencies associated with different sets of orientation parameters can differ significantly, and rigid body motion can be associated with non-zero oscillation frequencies, depending on the coordinates used.
A time-domain solution of the linearized equations is also presented in order to compare between the solutions obtained using two different sets of orientation parameters and also to shed light on the important issue of using the eigenvalue analysis in the study of MBS stability.
This resulted in 6 sets of orientation tuning curves: for low, medium and high contrast in the mixed contrasts condition, for low, medium and high contrast in the constant contrast condition, restricted to the adapted response only.
The fundamental domain of this tiling of the cortical plane is the hypercolumn, which contains two sets of orientation preferences θ ∈ [0, π) per eye, organised around a pair of orientation singularities or pinwheels [ 37].
To be rigorous the set of orientations should be identified with the projective line (P^{1}(mathbb {R})).
Here, we report a class of cells whose spatially periodic firing patterns are composed of plane waves (or bands) drawn from a discrete set of orientations and wavelengths.
Finally, we also explore the benefits of combining the 3D DDWT with the standard DWT to capture a wider set of orientations.
