An xy-Cartesian coordinate system rotated through an angle to an x′y′-Cartesian coordinate system
For broader coverage of this topic, see Rotations in two dimensions.
In mathematics, a rotation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x′y′-Cartesian coordinate system in which the origin is kept fixed and the x′ and y′ axes are obtained by rotating the x and y axes counterclockwise through an angle . A point P has coordinates (x, y) with respect to the original system and coordinates (x′, y′) with respect to the new system.[1] In the new coordinate system, the point P will appear to have been rotated in the opposite direction, that is, clockwise through the angle . A rotation of axes in more than two dimensions is defined similarly.[2][3] A rotation of axes is a linear map[4][5] and a rigid transformation.
^Protter & Morrey (1970, p. 320)
^Anton (1987, p. 231)
^Burden & Faires (1993, p. 532)
^Anton (1987, p. 247)
^Beauregard & Fraleigh (1973, p. 266)
and 23 Related for: Rotation of axes in two dimensions information
angle θ {\displaystyle \theta } . A rotationofaxesin more than twodimensions is defined similarly. A rotationofaxes is a linear map and a rigid transformation...
three-dimensional rotations are parameterized for physics, or medicine, or chemistry, or other disciplines. When we include the option of world axes or body axes, 24...
In geometry, various formalisms exist to express a rotationin three dimensions as a mathematical transformation. In physics, this concept is applied to...
figure at a center ofrotation. A solid figure has an infinite number of possible axes and angles ofrotation, including chaotic rotation (between arbitrary...
In the case of multiple mirror planes and/or axesofrotation, two symmetry groups are of the same symmetry type if and only if there is a rotation mapping...
an axis running from wing to wing; and roll, rotation about an axis running from nose to tail. The axes are alternatively designated as vertical, lateral...
ofrotations associated with simple bivectors in the algebra. Planes ofrotation are not used much intwo and three dimensions, as intwodimensions there...
the 3-fold axes are each through one vertex and the center of one face. Rotational symmetry with respect to any angle is, intwodimensions, circular symmetry...
composition ofrotations chained rotations. The geometrical definition demonstrates that three composed elemental rotations (rotations about the axesof a coordinate...
In numerical linear algebra, a Givens rotation is a rotationin the plane spanned by two coordinates axes. Givens rotations are named after Wallace Givens...
According to Euler's rotation theorem, simultaneous rotation along a number of stationary axes at the same time is impossible; if tworotations are forced at...
In ballistics and flight dynamics, axes conventions are standardized ways of establishing the location and orientation of coordinate axes for use as a...
perpendicular oriented lines, called coordinate lines, coordinate axes or just axes (plural of axis) of the system. The point where they meet is called the origin...
rotate in three dimensions, their moments can be described by a symmetric 3-by-3 matrix, with a set of mutually perpendicular principal axes for which...
case in which first and third axes are overlapping. The general problem of decomposing a rotation into three composed movements about intrinsic axes was...
axis of a composite rotation defined in terms of the axesof the tworotations. He derived this formula in 1840 (see page 408). The three rotationaxes A...
octahedral group) has the rotationaxesof an octahedron or cube (three 4-fold axes, four 3-fold axes, and six diagonal 2-fold axes). Oh includes horizontal...
into simple mirror planes; Screw axes are converted into simple axesofrotation) Axesofrotation, rotoinversion axes and mirror planes remain unchanged...
axis of a composite rotation defined in terms of the axesof the tworotations. He derived this formula in 1840 (see page 408). The three rotationaxes A...
pseudovectors and vector quaternions in three dimensions. They can be used to generate rotationsin a space of any number ofdimensions, and are a useful tool for...
S_{n}^{2n}=E.} Rotationaxes, mirror planes and inversion centres are symmetry elements, not symmetry operations. The rotation axis of the highest order...
Global Information
