Where a, b and c are the semi-dimensions of the scalene ellipsoid
l/2, w/2 and t/2 respectively.
In this research, we focused on the kinematic evolution of the ore-bearing ductile shear zone in the Zagros Orogeny and applied strain ellipsoid
shape as a vector to the interpretation of structure and intensity of deformation.
We choose 6 different ellipsoids
(three of them are prolate and three are oblate).
Asada, "Dynamic analysis and design of robot manipulators using inertia ellipsoids
," in Proceedings of the 1984 IEEE International Conference on Robotics and Automation, pp.
Section 3 provides two new approaches for the estimation and prediction of the debris dispersion due to the breakup during the reentry which is introduced by propagating the covariances of positional probabilistic ellipsoids
. Section 4 shows performance comparisons of the proposed estimation approaches, that is, the statistical linear regression with the unscented transformation and the Gauss-Hermite cubature-based numerical approximation are demonstrated.
The inertia ellipsoid
S is defined by the equation [mathematical expression not reproducible], or equivalently [mathematical expression not reproducible] where [mathematical expression not reproducible].
Generally, they are based on the fact that this chamber possesses a similar geometry to the ellipsoid
of revolution, or, still, to a truncated prolate spheroid (TPS), implying that two of its axle shafts must have equal measures [4-9].
It gives the concentration ellipsoid
illustrated on figure 1.
Both of the two shape families, ellipsoids
as well as prisms, are represented with discrete number of similar particles characterised by an specific elongation factor [k.sub.elon], non-dimensional values of which are ranging between 10 and 0.1, i.e.
are tighter fitting than spheres for elongated objects, chiefly arms and legs in humanoid modeling; they are not invariant to rotations; however, their calculation and the test between ellipsoids
is more complex than spheres volumes (Arcila & Banon, 2005; Bing et al., 2009) (Figure 1 (f)).
The predominant type of phytoliths is "irregular ruminate" (57%), significantly few encountered phytoliths as "thinning rough parallelepiped with rounded edges" (10%) and "smooth ellipsoids