Читать книгу Kinematics of General Spatial Mechanical Systems - M. Kemal Ozgoren - Страница 42

Consider the following equation, in which is a specified rotation matrix expressed in an observation frame .

(2.114)

Most typically, is specified as an overall rotation matrix in a case of m successive rotations so that . Here, it is required to find the angle and axis, i.e. θ and , of the overall rotation operator. In order to find them, Eq. (2.114) can be written again in the following detailed form.

(2.115)

Equation (2.115) provides the following scalar equations.

(2.116)

(2.117)

(2.118)

(2.119)

(2.120)

(2.121)

(2.122)

(2.123)

(2.124)

Furthermore, the following three equations can be obtained from Eqs. (2.119)–(2.124).

(2.125)

(2.126)

(2.127)