Sentence examples for on a unit sphere from inspiring English sources

In the first step, position of a point on rigid body and orientation of a rigid body on a unit sphere are described.

where a ij,n ij are the area on a unit sphere and number of measurements for bin (i,j), respectively.

where the notations Δ S 2 and ∇ S 2 refer to the Laplace and divergence operators on a unit sphere, respectively.

The difference in the stress states is quantitatively evaluated by the angular stress distance on a unit sphere in a five-dimensional Euclidean space (Sato and Yamaji, 2006).

With this constraint, the CSF lies on a unit sphere, and can be represented in spherical coordinates: w0 ≜ w x = cos sin, w1 ≜ w z = cos, w2 ≜ w y = sin sin.

Ω is the solid angle of the cone with an apex angle 2θ0, which is the area of a spherical cap on a unit sphere, so that Ω is written as 2π(1 − cosθ0).

We let molecules diffuse freely on the surface of a unit sphere, and be absorbed by a small circular patch at one of the poles.

Here, for convenience, we use the coordinate system with a fixed object at the origin and a moving camera on the surface of a unit sphere (Fig. 2).

In our proposed method, the steering vector is expanded into a limited Fourier series of phase modes by considering an element on the surface of a unit sphere.

The Thomson problem dealt with the equilibrium positions of N unit point charges on the surface of a unit sphere.

In three dimensions, the PDF on the surface of a unit sphere is (Fisher, 1953; Mardia and Jupp, 1999): V (x ^ ; μ ^, κ ) = κ 2 π (e κ − e − κ ) e κ μ ^ · x ^ Using this distribution to transmit T ¯ j k + 1, we compute x ^ k + 1 as the direction cosines of the vector T ¯ j k + 1 − T ¯ j k, and μ ^ k + 1 as the direction cosines of the vector S i k + 1 − T ¯ j k.