Quaternions and rotation sequences. (English) Zbl 0993.53005

Kuipers, Jack B.

Mladenov, I. M. (ed.) et al., Proceedings of the international conference on geometry, integrability and quantization, Varna, Bulgaria, September 1-10, 1999. Sofia: Coral Press Scientific Publishing. 127-143 (2000).

It is well-known that rotations of the Euclidean 3-space can be represented in an elegant form in terms of quaternions, see, for example [I. L. Kantor and A. S. Solodownikow, Hyperkomplexe Zahlen. Leipzig: Teubner Verlag (1978; Zbl 0395.17001)]. The author contributes to the field by developing a so called “rotation sequences” machinery aimed at effective representation of an arbitrary rotation as a superposition of rotations around coordinate axes.
The main peculiarities of the article are as follows: 1) presentation is given on an elementary level and starts from the very beginning of the theory of quaternions; 2) no proofs are given; 3) some applications are discussed for the machinery proposed (such as design of satellite orbits and derivation of some formulas of the spherical trigonometry).
For the entire collection see [Zbl 0940.00039].

Reviewer: Victor Alexandrov (Novosibirsk)

MSC:

53A17	Differential geometric aspects in kinematics
70B10	Kinematics of a rigid body
70F15	Celestial mechanics

Keywords:

Hamiltons quaternions; quaternion algebra; rotation operator; open rotation sequence; closed rotation sequence; Euler angles; spherical triangle; spherical equilateral \(n\)-gon; weather satellite orbit

Citations:

Zbl 0395.17001