Rotation Math

       
           

With reference of mathematics, rotation is defined as motion of an object around a fixed point. Rotation is a transformation in plane of an object.  We can say that, rotations in math are transformation where an object rotates about a fixed point. Rotation Math is different from translation, in translation there is no rotation about a fixed point.
Rotations math can be express as rotation of an object where we can see changes only in coordinates of that object. When we rotate an object there is no change in shape of that object.
Rotation in math says that, fixed point can be either in object or outside object.

In rotation, we have to concentrate over the frame of reference of an object. For an example, if we rotate an object clockwise and if we rotate an object counter clockwise then both conditions will give different result.
When body is rotate then its angle of rotation is measured in terms of degree. There is a convention that angle which is measured in clockwise direction is a negative angle and angle which is measured in counter clockwise will be a positive angle.

Rotation in maths can be defined in two dimensional or three dimensional. Rotation in three dimensions is different from the rotation in two dimensions. For an example rotation in two dimensions will give same results as they are commutative in nature but rotations in three dimensions are not commutative, they will not give same result in every condition.
Just like two dimensional and three dimensional rotations, it can be multi dimensional rotations as well.
Rotations in maths are used in matrix algebra, Euler rotations, etc

Topics Covered in Rotation Math

Rotational Symmetry

When we change position of object about a fixed point then it is called as rotation. Rotational symmetry states that if object looks same as original after a rotation then it will have rotational symmetry.

 

Object or a body can have more than one rotational symmetry. For instance triskelon will appear same after rotation. When we turn or rotate th...Read More

Rotation Matrix

Rotation matrix can be used to demonstrate a rotation in linear algebra. For example:
 
 
 
In above given matrix, matrix rotation points are rotated in x-y Cartesian plane (here x – coordinate is along the horizontal axi...Read More

Math Topics