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25 relations: Angle, Angular distance, Angular velocity, Arc (geometry), Axis–angle representation, Charts on SO(3), Commutative property, Degree (angle), Euclidean vector, Euler angles, Euler's rotation theorem, Exponential map (Lie theory), Lie algebra, Linear elasticity, Matrix exponential, Projection (linear algebra), Radian, Right-hand rule, Rotation, Rotation around a fixed axis, Rotation group SO(3), Rotation matrix, Second moment of area, Skew-symmetric matrix, Turn (geometry).
Angle
In plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
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Angular distance
In mathematics (in particular geometry and trigonometry) and all natural sciences (e.g. astronomy and geophysics), the angular distance (angular separation, apparent distance, or apparent separation) between two point objects, as viewed from a location different from either of these objects, is the angle of length between the two directions originating from the observer and pointing toward these two objects.
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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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Arc (geometry)
In Euclidean geometry, an arc (symbol: ⌒) is a closed segment of a differentiable curve.
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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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Charts on SO(3)
In mathematics, the special orthogonal group in three dimensions, otherwise known as the rotation group SO(3), is a naturally occurring example of a manifold.
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Commutative property
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.
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Degree (angle)
A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle, defined so that a full rotation is 360 degrees.
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Euclidean vector
In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction.
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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's rotation theorem
In geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the rigid body remains fixed, is equivalent to a single rotation about some axis that runs through the fixed point.
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Exponential map (Lie theory)
In the theory of Lie groups, the exponential map is a map from the Lie algebra \mathfrak g of a Lie group G to the group, which allows one to recapture the local group structure from the Lie algebra.
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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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Linear elasticity
Linear elasticity is the mathematical study of how solid objects deform and become internally stressed due to prescribed loading conditions.
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Matrix exponential
In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function.
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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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Radian
The radian (SI symbol rad) is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics.
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Right-hand rule
In mathematics and physics, the right-hand rule is a common mnemonic for understanding orientation conventions for the vector cross product in three dimensions.
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Rotation
A rotation is a circular movement of an object around a center (or point) of rotation.
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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 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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Second moment of area
The 2nd moment of area, also known as moment of inertia of plane area, area moment of inertia, or second area moment, is a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis.
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Skew-symmetric matrix
In mathematics, particularly in linear algebra, a skew-symmetric (or antisymmetric or antimetric) matrix is a square matrix whose transpose equals its negative; that is, it satisfies the condition In terms of the entries of the matrix, if aij denotes the entry in the and; i.e.,, then the skew-symmetric condition is For example, the following matrix is skew-symmetric: 0 & 2 & -1 \\ -2 & 0 & -4 \\ 1 & 4 & 0\end.
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Turn (geometry)
A turn is a unit of plane angle measurement equal to 2pi radians, 360 degrees or 400 gradians.
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References
[1] https://en.wikipedia.org/wiki/Angular_displacement
