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Erschienen in:
2010 | OriginalPaper | Buchkapitel
Mathematical Preliminaries
verfasst von : Wen-Hong Zhu
Erschienen in: Virtual Decomposition Control
Verlag: Springer Berlin Heidelberg
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In this chapter, mathematical tools to be used throughout this book are given.
Starting from notation, this chapter presents spaces and groups first. After that, vectors and coordinate systems are introduced, particularly the body-frame referenced vector expressions are emphasized. Orientations expressed by quaternions are given. Then, linear/angular velocity vectors and force/moment vectors are defined, leading to the rigid body dynamics expressed in a body frame. Two functions to be used in the parameter adaptation are subsequently defined. Furthermore, the concept of the virtual decomposition is presented and the terminology of the
virtual
power
flow is introduced, giving rise to the definition of the
virtual
stability
in conjunction with a simple oriented graph. This chapter ends with a formal definition of algebraic loops.