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searching for Coordinate vector 48 found (80 total)

Vector (mathematics and physics) (2,694 words) [view diff] exact match in snippet view article

Euclidean vector space, and a vector space formed by tuples is called a coordinate vector space. Many vector spaces are considered in mathematics, such as extension

Mass matrix (1,147 words) [view diff] exact match in snippet view article find links to article

derivative q ˙ {\displaystyle \mathbf {\dot {q}} } of the generalized coordinate vector q of a system and the kinetic energy T of that system, by the equation

Standard basis (1,006 words) [view diff] exact match in snippet view article find links to article

standard basis (also called natural basis or canonical basis) of a coordinate vector space (such as R n {\displaystyle \mathbb {R} ^{n}} or C n {\displaystyle

Right-hand rule (2,359 words) [view diff] exact match in snippet view article find links to article

(third coordinate vector), then the fingers curl from the positive x-axis (first coordinate vector) toward the positive y-axis (second coordinate vector).

Kinematics (9,219 words) [view diff] exact match in snippet view article find links to article

trajectory of particles. The position of a particle is defined as the coordinate vector from the origin of a coordinate frame to the particle. For example

Affine manifold (982 words) [view diff] exact match in snippet view article find links to article

structure are called affine charts. In each affine coordinate domain the coordinate vector fields form a parallelisation of that domain, so there is an associated

Matrix representation of conic sections (3,254 words) [view diff] exact match in snippet view article find links to article

{x} =0,} where x {\displaystyle \mathbf {x} } is the homogeneous coordinate vector in three variables restricted so that the last variable is 1, i.e

Lever (2,397 words) [view diff] exact match in snippet view article find links to article

operated by applying an input force FA at a point A located by the coordinate vector rA on the bar. The lever then exerts an output force FB at the point

Scalar (mathematics) (1,046 words) [view diff] exact match in snippet view article

every vector space over a field K is isomorphic to the corresponding coordinate vector space where each coordinate consists of elements of K (E.g., coordinates

Rigid rotor (6,099 words) [view diff] exact match in snippet view article find links to article

&0\\0&0&1\end{pmatrix}}} Let r ( 0 ) {\displaystyle \mathbf {r} (0)} be the coordinate vector of an arbitrary point P {\displaystyle {\mathcal {P}}} in the body

Quantum amplifier (1,855 words) [view diff] exact match in snippet view article find links to article

} {\displaystyle ~{\vec {x}}=\{x_{1},x_{2},z\}~} is the spatial coordinate vector, with z giving the direction of motion, e → {\displaystyle ~{\vec

Schwarzschild coordinates (4,089 words) [view diff] exact match in snippet view article find links to article

chart for the exterior region of the Kerr vacuum, where the timelike coordinate vector is not hypersurface orthogonal.) Note the last two fields are rotations

Moving frame (2,587 words) [view diff] exact match in snippet view article find links to article

each vector field ej can be expressed as a linear combination of the coordinate vector fields ∂ ∂ x i {\textstyle {\frac {\partial }{\partial x^{i}}}} :

Ricci curvature (5,863 words) [view diff] exact match in snippet view article find links to article

{\displaystyle g_{ij}} are defined by evaluating g {\displaystyle g} on coordinate vector fields, while the functions g i j {\displaystyle g^{ij}} are defined

Molecular Hamiltonian (5,204 words) [view diff] exact match in snippet view article find links to article

})^{2}+(z_{i}-z_{j})^{2}}}.} In this expression ri stands for the coordinate vector of any particle (electron or nucleus), but from here on we will reserve

Scaling (geometry) (1,609 words) [view diff] exact match in snippet view article

To scale an object by a vector v = (vx, vy, vz), each homogeneous coordinate vector p = (px, py, pz, 1) would need to be multiplied with this projective

Lie bracket of vector fields (1,956 words) [view diff] exact match in snippet view article find links to article

{\displaystyle M} , with X {\displaystyle X} and Y {\displaystyle Y} as coordinate vector fields: Theorem: [ X , Y ] = 0 {\displaystyle [X,Y]=0\,} iff the flows

Virtual work (6,348 words) [view diff] exact match in snippet view article find links to article

operated by applying an input force FA at a point A located by the coordinate vector rA on the bar. The lever then exerts an output force FB at the point

Curvature of Riemannian manifolds (2,115 words) [view diff] exact match in snippet view article find links to article

⁠ v = ∂ / ∂ x j {\displaystyle v=\partial /\partial x_{j}} ⁠ are coordinate vector fields then ⁠ [ u , v ] = 0 {\displaystyle [u,v]=0} ⁠ and therefore

Luke's variational principle (2,743 words) [view diff] exact match in snippet view article find links to article

g is the acceleration by the Earth's gravity, x is the horizontal coordinate vector with components x and y, x and y are the horizontal coordinates, z

Fundamental theorem of Riemannian geometry (2,105 words) [view diff] exact match in snippet view article find links to article

to the first Christoffel identity in the case that X, Y, and Z are coordinate vector fields. The equations displayed above can be rearranged to produce

Transformation matrix (3,815 words) [view diff] exact match in snippet view article find links to article

When using affine transformations, the homogeneous component of a coordinate vector (normally called w) will never be altered. One can therefore safely

Levi-Civita connection (3,432 words) [view diff] exact match in snippet view article find links to article

indices. As one checks by taking for X , Y , Z {\displaystyle X,Y,Z} , coordinate vector fields ∂ j , ∂ k , ∂ l {\displaystyle \partial _{j},\partial _{k}

Riemann curvature tensor (2,934 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \partial _{\mu }=\partial /\partial x^{\mu }} are the coordinate vector fields. The above expression can be written using Christoffel symbols:

Reynolds stress (2,250 words) [view diff] exact match in snippet view article find links to article

direction (with x i {\displaystyle x_{i}} denoting the components of the coordinate vector x {\displaystyle \mathbf {x} } ). The mean velocities u i ¯ {\displaystyle

Conformal geometry (3,359 words) [view diff] exact match in snippet view article find links to article

q) ⊕ (Rn)∗. The stabilizer of the null ray pointing up the last coordinate vector is given by the Borel subalgebra h = g0 ⊕ g1. Conformal geometric

2D computer graphics (3,988 words) [view diff] exact match in snippet view article find links to article

To scale an object by a vector v = (vx, vy, vz), each homogeneous coordinate vector p = (px, py, pz, 1) would need to be multiplied with this projective

Tetrad formalism (2,959 words) [view diff] exact match in snippet view article find links to article

defines a genuine tensor when differentiation is involved. Since the coordinate vector fields have vanishing Lie bracket (i.e. commute: ∂ μ ∂ ν = ∂ ν ∂ μ

Minkowski space (10,458 words) [view diff] exact match in snippet view article find links to article

with f = xμ, the coordinate function itself, and X = ∂/∂xν, called a coordinate vector field, one obtains d x μ ( ∂ ∂ x ν ) = ∂ x μ ∂ x ν = δ ν μ . {\displaystyle

Shear mapping (1,911 words) [view diff] exact match in snippet view article find links to article

the roles of x and y are swapped. It corresponds to multiplying the coordinate vector by the transposed matrix: ( x ′ y ′ ) = ( x m x + y ) = ( 1 0 m 1

Digital image processing (5,364 words) [view diff] exact match in snippet view article find links to article

usually 1, so that the new coordinate is [x, y, 1]. This allows the coordinate vector to be multiplied by a 3×3 matrix, enabling translation shifts. Thus

Frame bundle (3,035 words) [view diff] exact match in snippet view article find links to article

coordinates ( x 1 , … , x n ) {\displaystyle (x^{1},\ldots ,x^{n})} the coordinate vector fields ( ∂ ∂ x 1 , … , ∂ ∂ x n ) {\displaystyle \left({\frac {\partial

Distribution (differential geometry) (3,880 words) [view diff] exact match in snippet view article

M=\mathbb {R} ^{n}} is generated by the first k {\displaystyle k} coordinate vector fields ∂ ∂ x 1 , … , ∂ ∂ x k {\displaystyle {\frac {\partial }{\partial

Acoustoelastic effect (6,219 words) [view diff] exact match in snippet view article find links to article

point is defined by the coordinate vector X {\displaystyle {\boldsymbol {X}}} while the same point has the coordinate vector x {\displaystyle {\boldsymbol

Curl (mathematics) (5,050 words) [view diff] exact match in snippet view article

{\partial x_{3}}{\partial u_{i}}}\right)^{2}}}} is the length of the coordinate vector corresponding to ui. The remaining two components of curl result from

Thom's first isotopy lemma (980 words) [view diff] exact match in snippet view article find links to article

{\displaystyle N=\mathbb {R} ^{n}} and ∂ i {\displaystyle \partial _{i}} the coordinate vector fields on R n {\displaystyle \mathbb {R} ^{n}} . Then, by the lifting

Kaczmarz method (4,851 words) [view diff] exact match in snippet view article find links to article

and S {\displaystyle S} to be the i t h {\displaystyle i^{th}} unit coordinate vector with probability p i = ‖ a i ‖ 2 2 / ‖ A ‖ F 2 . {\displaystyle

Generalized coordinates (4,543 words) [view diff] exact match in snippet view article find links to article

a circle of radius L. The position of the mass is defined by the coordinate vector r = (x, y) measured in the plane of the circle such that y is in the

Line–line intersection (4,002 words) [view diff] exact match in snippet view article find links to article

of n lines can be represented by 2n equations in the 3-dimensional coordinate vector w: A w = b {\displaystyle \mathbf {A} \mathbf {w} =\mathbf {b} } where

Covariance and contravariance of vectors (7,130 words) [view diff] exact match in snippet view article find links to article

of covariance and contravariance refers to how the components of a coordinate vector transform under a change of basis (passive transformation). Thus let

Dual quaternion (4,786 words) [view diff] exact match in snippet view article find links to article

quaternions, the product ÂĈ can be viewed as the operation of Ĉ on the coordinate vector Â, which means ÂĈ can also be formulated as, A ^ C ^ = [ C ^ − ] A

Euler's rotation theorem (4,497 words) [view diff] exact match in snippet view article find links to article

one-to-one correspondence with a 3 × 3 rotation matrix R that transforms a coordinate vector x into X, that is Rx = X. Therefore, another version of Euler's theorem

Quaternion (12,648 words) [view diff] exact match in snippet view article find links to article

j, and k. The vector part of a quaternion can be interpreted as a coordinate vector in R 3 ; {\displaystyle \mathbb {R} ^{3};} therefore, the algebraic

D'Alembert's paradox (4,215 words) [view diff] exact match in snippet view article find links to article

it is of the form u(x, t) = u(x − v t, 0), where x is the spatial coordinate vector, and thus: ∂ u ∂ t + ( v ⋅ ∇ ) u = 0 . {\displaystyle {\frac {\partial

Christoffel symbols (8,239 words) [view diff] no match in snippet view article find links to article

R n {\displaystyle \mathbb {R} ^{n}} pulls back to a standard ("coordinate") vector basis ( ∂ 1 , ⋯ , ∂ n ) {\displaystyle (\partial _{1},\cdots ,\partial

Discrete Laplace operator (5,716 words) [view diff] exact match in snippet view article find links to article

continuous function f ( r ¯ ) {\displaystyle f({\bar {r}})} , where the coordinate vector r ¯ ∈ R n {\displaystyle {\bar {r}}\in R^{n}} and the value domain

Quadrature based moment methods (1,730 words) [view diff] exact match in snippet view article find links to article

external coordinates of time and space respectively, while the internal coordinate vector, ξ {\displaystyle \mathbf {\xi } } , may contain any additional desired

Creep and shrinkage of concrete (4,305 words) [view diff] exact match in snippet view article find links to article

{\displaystyle h(\mathbf {x} ,t)} ( x {\displaystyle \mathbf {x} } = coordinate vector) may be approximately considered as uncoupled from the stress and