Search results
Results from the WOW.Com Content Network
In geodesy, geographic coordinate conversion is defined as translation among different coordinate formats or map projections all referenced to the same geodetic datum. [1] A geographic coordinate transformation is a translation among different geodetic datums. Both geographic coordinate conversion and transformation will be considered in this ...
The direct-quadrature-zero (DQZ, DQ0 [1] or DQO, [2] sometimes lowercase) transformation or zero-direct-quadrature [3] (0DQ or ODQ, sometimes lowercase) transformation is a tensor that rotates the reference frame of a three-element vector or a three-by-three element matrix in an effort to simplify analysis.
In mathematics, the indefinite orthogonal group, O(p, q) is the Lie group of all linear transformations of an n-dimensional real vector space that leave invariant a nondegenerate, symmetric bilinear form of signature (p, q), where n = p + q. It is also called the pseudo-orthogonal group [1] or generalized orthogonal group. [2]
Then the distance between and is given by: [2] d ( p , q ) = ( p 1 − q 1 ) 2 + ( p 2 − q 2 ) 2 . {\displaystyle d(p,q)={\sqrt {(p_{1}-q_{1})^{2}+(p_{2}-q_{2})^{2}}}.} This can be seen by applying the Pythagorean theorem to a right triangle with horizontal and vertical sides, having the line segment from p {\displaystyle p} to q ...
In fluid dynamics, dynamic pressure (denoted by q or Q and sometimes called velocity pressure) is the quantity defined by: [1] = where (in SI units): q is the dynamic pressure in pascals (i.e., N/m 2, ρ (Greek letter rho) is the fluid mass density (e.g. in kg/m 3), and; u is the flow speed in m/s.
where R 1 is an n×n upper triangular matrix, 0 is an (m − n)×n zero matrix, Q 1 is m×n, Q 2 is m×(m − n), and Q 1 and Q 2 both have orthogonal columns. Golub & Van Loan (1996, §5.2) call Q 1 R 1 the thin QR factorization of A; Trefethen and Bau call this the reduced QR factorization. [1] If A is of full rank n and we require that the ...
The resulting orientation of Body 3-2-1 sequence (around the capitalized axis in the illustration of Tait–Bryan angles) is equivalent to that of lab 1-2-3 sequence (around the lower-cased axis), where the airplane is rolled first (lab-x axis), and then nosed up around the horizontal lab-y axis, and finally rotated around the vertical lab-z ...
Any (p,q)-torus knot can be made from a closed braid with p strands. The appropriate braid word is [8] (). (This formula assumes the common convention that braid generators are right twists, [4] [8] [9] [10] which is not followed by the Wikipedia page on braids.) The crossing number of a (p,q) torus knot with p,q > 0 is given by c = min((p−1 ...