Rotation in 3D Space

Authored by: Ayman F. Habib

Multisensor Attitude Estimation

Print publication date:  August  2016
Online publication date:  November  2016

Print ISBN: 9781498745710
eBook ISBN: 9781315368795
Adobe ISBN:


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Rotation in space is an important concept that is crucial for mapping activities, in general, and navigation applications, in particular. Rotation in space can be defined with the help of rotation matrices, which describe the mathematical relationship between two coordinate systems that might not be parallel to each other. Such rotation matrices can be derived through a sequence of rotation angles around the cardinal axes of a given coordinate system to produce another one. This approach is known as rotation derivation using Euler angles. Alternatively, rotation in space can be defined through a single rotation around an axis in space. One way of defining the rotation-axis/rotation-angle pair is quaternion. This chapter will discuss both Euler angles and quaternion approaches for defining rotation in space as well as their characteristics. Before introducing the alternative approaches for describing rotation, we will briefly discuss the coordinate systems that are mainly encountered in navigation applications.

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