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In mathematics, a moving frame is a flexible generalization of the notion of an ordered basis of a vector space often used to study the extrinsic differential geometry of smooth manifolds embedded in a homogeneous space . Introduction.
9 KINEMATICS OF MOVING FRAMES. An understanding of inertial guidance systems for navigation of vehicles and robots requires some background in kinematics. Central in our discussion is the use of multiple reference frames. Such frames surround us in our daily lives: Earth latitude and longitude. Forward, backward motion relative to current position.
Learn about the new, algorithmic theory of moving frames, a powerful tool for studying geometric properties and invariants under transformation groups. The paper surveys applications in geometry, computer vision, invariant theory, and numerical analysis.
Learn about the equivariant method of moving frames for finite-dimensional Lie group actions, with applications to geometry, differential equations, computer vision, and more. The article surveys the theory, algorithms, and history of this powerful tool for analyzing symmetry and invariants.
- 341KB
- 35
Jul 5, 2011 · This chapter presents the equivariant method of moving frames for finite-dimensional Lie group actions, surveying a variety of applications, including geometry, differential equations, computer vision, numerical analysis, the calculus of variations, and invariant flows.
- Peter J. Olver
- 2009
System Design for Uncertainty (Hover and Triantafyllou) We discuss kinematics, focusing on transformation of vectors through change of reference frame, as a background to understanding inertial guidance systems for vehicles and robots.
We first describe how to transform vectors through changes in reference frame. Considering differential rotations over differential time elements gives rise to the concept of the rotation vector, which is used in deriving inertial dynamics in a moving body frame.
