This monitoring has become a mandatory practice implemented by OSHA, in an effort to protect workers from their work environment and ensure proper rotation of work duties ( i . e . rotating employees from a high exposure position to a low exposure position ).
32.
In the wider sense, a proper rotation is defined as a "'direct isometry "'; i . e ., an element of " E " + ( 3 ) : it can also be the identity, a rotation with a translation along the axis, or a pure translation.
33.
The investigators also requested that Fokker conduct a study of the effects of ice contamination and pilot technique on the F28 aircraft . The NTSB evaluated the data from the tests and found that the pilot initiated the rotation five knots earlier at 119 knots instead of the proper rotation speed of 124 knots.
34.
It therefore can be identified as a rotation or rotoreflection; is called a rotor if it is a proper rotation ( as it is if it can be expressed as a product of an even number of vectors ) and is an instance of what is known in GA as a " versor " ( presumably for historical reasons ).
35.
However, one can also consider improper rotations, i . e . a mirror-reflection possibly followed by a proper rotation . ( One example of an improper rotation is inversion through a point in 3-dimensional space . ) Suppose everything in the universe undergoes an improper rotation described by the rotation matrix " R ", so that a position vector "'x "'is transformed to.
36.
The set of all proper rotations ( about any angle ) through any axis of a sphere form a Lie group called the special orthogonal group \, SO ( 3 ) . ( The " 3 " refers to the three-dimensional space of an ordinary sphere . ) Thus, the symmetry group of the sphere with proper rotations is \, SO ( 3 ).
37.
The set of all proper rotations ( about any angle ) through any axis of a sphere form a Lie group called the special orthogonal group \, SO ( 3 ) . ( The " 3 " refers to the three-dimensional space of an ordinary sphere . ) Thus, the symmetry group of the sphere with proper rotations is \, SO ( 3 ).
