Sentence examples for by the unit vector from inspiring English sources

The radial movement can be described by the unit vector for the component, the horizontal rotation by the unit vector for the component, and the vertical movement by the unit vector for the component.

B k represents the kth agent and all the bodies are fixed in the Cartesian reference frame which is denoted by the unit vector (N1, N2).

A pulsatile kick in the direction given by the unit vector w (see (9)) causes a change in the amplitude variable.

Let us assume that a pulse of small modulus ϵ instantaneously displaces the trajectory in a direction given by the unit vector w.

The theoretical basis is the idea of a tube segment of unit length and orientation given by the unit vector In the stress-free state, u is deformed into in the current state.

The rotation generator (hat {sigma }_{hat {mathbf {n}}} equiv hat {mathbf {n}}cdot boldsymbol {sigma }equiv n_{x}hat {sigma }_{x}+n_{y}hat {sigma }_{y}+n_{z}hat {sigma }_{z}) produces a rotation though an angle θ about the axis defined by the unit vector (hat {mathbf {n}}inmathbb{R}^{3}).

The magnetic field vector is denoted by B, its absolute value by B and the unit vector by b.

Still, the quaternions can be regarded as a four-dimensional vector space formed by combining a real number with a three-dimensional vector, with a basis (set of generating vectors) given by the unit vectors 1, i, j, and k such that i2 = j2 = k2 = ijk = −1.

The lattice is obtained by translating the unit cell 0 by the unit vectors (mathbf{v}_{1}) and (mathbf{v}_{2}).

We denote by e i the unit vector whose i-th entry equals 1 and by 1 the 'one' vector whose components all equal 1.

According to equation (A.6) of Amm and Viljanen (1999), the vector potential of a divergence-free SECS below the current layer (ionosphere) is given by (B.1)Here the unit vector êφ, is given in the coordinate system centered at the SECS pole.