BSNS102 Study Guide - Final Guide: Global Positioning System, Cross Product, Standard-Definition Television

• School: University of Otago
• Department: Business Studies
• Course: BSNS102
• Professor: Drew Stelljes

Document Summary

Recalling the restriction that n has unit length, we have: Applying the trig identity sin2x + cos2x = 1 (see appendix a): For our purposes of using quaternions to represent orientation, we will only deal with so-called unit quaternions that obey this rule. For information concerning non-normalized quaternions, we refer the reader to [3]. The conjugate of a quaternion, denoted q*, is obtained by negating the vector portion of the quaternion: The inverse of a quaternion, denoted q 1, is defined as the conjugate of a quaternion divided by its magnitude: The quaternion inverse has an interesting correspondence with the multiplicative inverse for real numbers (scalars). For real numbers, the multiplicative inverse a 1 is 1/a. In other words, a(a 1) = a 1a = 1. When we multiply a quaternion q by its inverse q 1, we get the identity quaternion [1, 0]. (we will discuss quaternion multiplication in the next section. )