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A rotating frame of reference is a special case of a non-inertial reference frame that is rotating relative to an inertial reference frame. An everyday example of a rotating reference frame is the surface of the Earth. (This article considers only frames rotating about a fixed axis. For more general rotations, see Euler angles.)
One may instead change to a coordinate frame fixed in the rotating body, in which the moment of inertia tensor is constant. Using a reference frame such as that at the center of mass, the frame's position drops out of the equations. In any rotating reference frame, the time derivative must be replaced so that the equation becomes
Let (x, y, z) the Cartesian coordinate system of the laboratory (or stationary) frame of reference, and (x′, y′, z′) = (x′, y′, z) be a Cartesian coordinate system that is rotating around the z axis of the laboratory frame of reference with angular frequency Ω. This is called the rotating frame of reference. Physical variables in ...
These derivative formulas now are applied to the relationship between acceleration in an inertial frame, and that in a coordinate frame rotating with time-varying angular velocity ω(t). From the previous section, where subscript A refers to the inertial frame and B to the rotating frame, setting a AB = 0 to remove any translational ...
The axes of the original frame are denoted as x, y, z and the axes of the rotated frame as X, Y, Z.The geometrical definition (sometimes referred to as static) begins by defining the line of nodes (N) as the intersection of the planes xy and XY (it can also be defined as the common perpendicular to the axes z and Z and then written as the vector product N = z × Z).
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.
The first attempt to represent an orientation is attributed to Leonhard Euler.He imagined three reference frames that could rotate one around the other, and realized that by starting with a fixed reference frame and performing three rotations, he could get any other reference frame in the space (using two rotations to fix the vertical axis and another to fix the other two axes).
In classical mechanics, the Euler force is the fictitious tangential force [1] that appears when a non-uniformly rotating reference frame is used for analysis of motion and there is variation in the angular velocity of the reference frame's axes.