Abstract
This chapter has shown that behind the use of Lie groups for rigid body motions, there are implicit assumptions that, even if more or less “natural”, are not intrinsic and just depend on a choice of relative reference between spaces (see Remark. 1.2.2, p.14).
It is always important to pinpoint those assumptions which are not intrinsic: any hypothesis which is not intrinsic can in fact be considered a modeling hypothesis and should be made explicit as such.
Twists have been analyzed in detail and their mappings and relations have been shown. The intrinsic mappings using right translations are the ones which give the motion of a space with respect to an observer space directly and have been denoted with only one subscript and one superscript: t j i or t i j .
A complete formal relation between the Lie group approach and Screw theory has then been presented. This one-to-one relation between the Lie group approach and the screw approach is due to the existence of two biinvariant forms known as the Killing form and the Hyperbolic or Klijn form.
The space of screw is equivalent in this way to the projectivization of the Lie algebra of rigid body motions.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
Rights and permissions
Copyright information
© 2001 Springer-Verlag London Limited
About this chapter
Cite this chapter
(2001). Rigid bodies and motions. In: Modeling and IPC control of interactive mechanical systems — A coordinate-free approach. Lecture Notes in Control and Information Sciences, vol 266. Springer, London. https://doi.org/10.1007/BFb0110401
Download citation
DOI: https://doi.org/10.1007/BFb0110401
Published:
Publisher Name: Springer, London
Print ISBN: 978-1-85233-395-9
Online ISBN: 978-1-84628-571-4
eBook Packages: Springer Book Archive