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3.7 Expression of a Transformation Matrix in a Case of Several Successive Rotations

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Suppose a reference frame is rotated into another reference frame through several successive rotations as described below.

(3.75)

In such a rotational sequence, the overall transformation matrix can be obtained as follows:

(3.76)

The matrix can be related to the rotation operators that appear in Description (3.75) through two different commonly used formulations depending on the reference frames in which the rotation operators are expressed. These two formulations are explained below.

Kinematics of General Spatial Mechanical Systems

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