Kinematics of General Spatial Mechanical Systems. M. Kemal Ozgoren

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Название Kinematics of General Spatial Mechanical Systems
Автор произведения M. Kemal Ozgoren
Жанр Математика
Серия
Издательство Математика
Год выпуска 0
isbn 9781119195764



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      (2.95)equation

      The corresponding vector equations can be written as follows, like those written for images and images:

      (2.96)equation

      (2.97)equation

      2.8.2 Example 2.2

      Consider three vectors represented by the column matrices images, images, and images in a reference frame images. Let these vectors be such that

      Let the same vectors be rotated by the rotation operator represented by images so that

      (2.100)equation

      (2.103)equation

      Hence, it is seen that

      (2.105)equation

      2.8.3 Example 2.3

      Starting with Eq. (2.75), the powers of images can be expressed as follows:

equation equation equation

      Thus, for all k ≥ 0, it happens that

      On the other hand, the following Taylor series expansion can be written for images.

      (2.109)equation

      2.8.4 Example 2.4

      For ijk = 123, Eq. (2.87) becomes