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2. Rotation matrix - Wikipedia

   en.wikipedia.org/wiki/Rotation_matrix

   The case of θ = φ is called an isoclinic rotation, having eigenvalues e ±iθ repeated twice, so every vector is rotated through an angle θ. The trace of a rotation matrix is equal to the sum of its eigenvalues. For n = 2, a rotation by angle θ has trace 2 cos θ. For n = 3, a rotation around any axis by angle θ has trace 1 + 2 cos θ.

3. Rotation formalisms in three dimensions - Wikipedia

   en.wikipedia.org/wiki/Rotation_formalisms_in...

   Rotation formalisms are focused on proper (orientation-preserving) motions of the Euclidean space with one fixed point, that a rotation refers to.Although physical motions with a fixed point are an important case (such as ones described in the center-of-mass frame, or motions of a joint), this approach creates a knowledge about all motions.

4. Rotation (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Rotation_(mathematics)

   The rotation group is a Lie group of rotations about a fixed point. This (common) fixed point or center is called the center of rotation and is usually identified with the origin. The rotation group is a point stabilizer in a broader group of (orientation-preserving) motions. For a particular rotation: The axis of rotation is a line of

5. Rotary table - Wikipedia

   en.wikipedia.org/wiki/Rotary_table

   Rotary tables are most commonly mounted "flat", with the table rotating around a vertical axis, in the same plane as the cutter of a vertical milling machine.An alternate setup is to mount the rotary table on its end (or mount it "flat" on a 90° angle plate), so that it rotates about a horizontal axis.

6. Rotary stage - Wikipedia

   en.wikipedia.org/wiki/Rotary_stage

   A rotary stage is a component of a motion system used to restrict an object to a single axis of rotation. The terms rotary table or rotation stage are often used interchangeably with rotary stage. All rotary stages consist of a platform and a base, joined by some form of guide in such a way that the platform is restricted to rotation about a ...

7. 3D rotation group - Wikipedia

   en.wikipedia.org/wiki/3D_rotation_group

   Every non-trivial rotation is determined by its axis of rotation (a line through the origin) and its angle of rotation. Rotations are not commutative (for example, rotating R 90° in the x-y plane followed by S 90° in the y-z plane is not the same as S followed by R ), making the 3D rotation group a nonabelian group .

8. Round-robin tournament - Wikipedia

   en.wikipedia.org/wiki/Round-robin_tournament

   Another disadvantage, especially in smaller round-robins, is the "circle of death", where teams cannot be separated on a head-to-head record. In a three-team round-robin, where A defeats B, B defeats C, and C defeats A, all three competitors will have a record of one win and one loss, and a tiebreaker will need to be used to separate the teams ...

9. Orientation (vector space) - Wikipedia

   en.wikipedia.org/wiki/Orientation_(vector_space)

   A vector space with an orientation selected is called an oriented vector space, while one not having an orientation selected, is called unoriented. In mathematics , orientability is a broader notion that, in two dimensions, allows one to say when a cycle goes around clockwise or counterclockwise, and in three dimensions when a figure is left ...