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43 relations: Angular velocity, Axis–angle representation, Cartesian coordinate system, Characteristic polynomial, Complex conjugate, Complex number, Computer graphics, Determinant, Direction cosine, Eigenvalues and eigenvectors, Equivalence relation, Euler angles, Euler–Rodrigues formula, Fixed point (mathematics), Geometry, Group (mathematics), Improper rotation, Instant centre of rotation, Kernel (linear algebra), Kinematics, Leonhard Euler, Lie algebra, Normal operator, Orthogonal matrix, Plane of rotation, Projection (linear algebra), Quaternion, Rigid body, Rotation (mathematics), Rotation around a fixed axis, Rotation formalisms in three dimensions, Rotation group SO(3), Rotation matrix, Round-off error, Screw axis, Screw theory, Spherical geometry, Spherical trigonometry, Three-dimensional space, Trace (linear algebra), Unit vector, Vector (mathematics and physics), William Rowan Hamilton.
Angular velocity
In physics, the angular velocity of a particle is the rate at which it rotates around a chosen center point: that is, the time rate of change of its angular displacement relative to the origin.
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Axis–angle representation
In mathematics, the axis–angle representation of a rotation parameterizes a rotation in a three-dimensional Euclidean space by two quantities: a unit vector indicating the direction of an axis of rotation, and an angle describing the magnitude of the rotation about the axis.
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Cartesian coordinate system
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
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Characteristic polynomial
In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues as roots.
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Complex conjugate
In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign.
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Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
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Computer graphics
Computer graphics are pictures and films created using computers.
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Determinant
In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.
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Direction cosine
In analytic geometry, the direction cosines (or directional cosines) of a vector are the cosines of the angles between the vector and the three coordinate axes.
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Eigenvalues and eigenvectors
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.
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Equivalence relation
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.
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Euler angles
The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body with respect to a fixed coordinate system.
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Euler–Rodrigues formula
In mathematics and mechanics, the Euler–Rodrigues formula describes the rotation of a vector in three dimensions.
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Fixed point (mathematics)
In mathematics, a fixed point (sometimes shortened to fixpoint, also known as an invariant point) of a function is an element of the function's domain that is mapped to itself by the function.
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Geometry
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
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Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.
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Improper rotation
In geometry, an improper rotation,.
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Instant centre of rotation
The instant center of rotation, also called instantaneous velocity center, or also instantaneous center or instant center, is the point fixed to a body undergoing planar movement that has zero velocity at a particular instant of time.
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Kernel (linear algebra)
In mathematics, and more specifically in linear algebra and functional analysis, the kernel (also known as null space or nullspace) of a linear map between two vector spaces V and W, is the set of all elements v of V for which, where 0 denotes the zero vector in W. That is, in set-builder notation,.
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Kinematics
Kinematics is a branch of classical mechanics that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the mass of each or the forces that caused the motion.
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Leonhard Euler
Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.
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Lie algebra
In mathematics, a Lie algebra (pronounced "Lee") is a vector space \mathfrak g together with a non-associative, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g; (x, y) \mapsto, called the Lie bracket, satisfying the Jacobi identity.
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Normal operator
In mathematics, especially functional analysis, a normal operator on a complex Hilbert space H is a continuous linear operator N: H → H that commutes with its hermitian adjoint N*, that is: NN*.
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Orthogonal matrix
In linear algebra, an orthogonal matrix is a square matrix whose columns and rows are orthogonal unit vectors (i.e., orthonormal vectors), i.e. where I is the identity matrix.
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Plane of rotation
In geometry, a plane of rotation is an abstract object used to describe or visualize rotations in space.
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Projection (linear algebra)
In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.
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Quaternion
In mathematics, the quaternions are a number system that extends the complex numbers.
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Rigid body
In physics, a rigid body is a solid body in which deformation is zero or so small it can be neglected.
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Rotation (mathematics)
Rotation in mathematics is a concept originating in geometry.
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Rotation around a fixed axis
Rotation around a fixed axis or about a fixed axis of revolution or motion with respect to a fixed axis of rotation is a special case of rotational motion.
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Rotation formalisms in three dimensions
In geometry, various formalisms exist to express a rotation in three dimensions as a mathematical transformation.
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Rotation group SO(3)
In mechanics and geometry, the 3D rotation group, often denoted SO(3), is the group of all rotations about the origin of three-dimensional Euclidean space R3 under the operation of composition.
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Rotation matrix
In linear algebra, a rotation matrix is a matrix that is used to perform a rotation in Euclidean space.
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Round-off error
A round-off error, also called rounding error, is the difference between the calculated approximation of a number and its exact mathematical value due to rounding.
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Screw axis
A screw axis (helical axis or twist axis) is a line that is simultaneously the axis of rotation and the line along which translation of a body occurs.
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Screw theory
Screw theory is the algebra and calculus of pairs of vectors, such as forces and moments and angular and linear velocity, that arise in the kinematics and dynamics of rigid bodies.
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Spherical geometry
Spherical geometry is the geometry of the two-dimensional surface of a sphere.
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Spherical trigonometry
Spherical trigonometry is the branch of spherical geometry that deals with the relationships between trigonometric functions of the sides and angles of the spherical polygons (especially spherical triangles) defined by a number of intersecting great circles on the sphere.
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Three-dimensional space
Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point).
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Trace (linear algebra)
In linear algebra, the trace of an n-by-n square matrix A is defined to be the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of A, i.e., where aii denotes the entry on the ith row and ith column of A. The trace of a matrix is the sum of the (complex) eigenvalues, and it is invariant with respect to a change of basis.
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Unit vector
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.
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Vector (mathematics and physics)
When used without any further description, vector usually refers either to.
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William Rowan Hamilton
Sir William Rowan Hamilton MRIA (4 August 1805 – 2 September 1865) was an Irish mathematician who made important contributions to classical mechanics, optics, and algebra.
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Euler Pole, Euler fixed point theorem, Euler rotation theorem, Euler's fixed point theorem.
References
[1] https://en.wikipedia.org/wiki/Euler's_rotation_theorem
