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Lecture L3 - Vectors, Matrices and Coordinate Transformations. By using vectors and defining appropriate operations between them, physical laws can often be written in a simple form. Since we will making extensive use of vectors in Dynamics, we will summarize some of their important properties.
28 cze 2021 · Matrix mechanics, described in appendix \(19.1\), provides the most convenient way to handle coordinate rotations. The transformation matrix, between coordinate systems having differing orientations is called the rotation matrix. This transforms the components of any vector with respect to one coordinate frame to the components with respect to ...
Make it very explicit what coordinate system is used. Understand how to change coordinate systems. Understand how to transform objects. Understand difference between points, vectors, normals and their coordinates.
1 Transformation by Matrices. We can represent general transformations of homogeneous coordinates by matrices. This idea has been used widely in geometric modeling to describe the relationships between objects.
This chapter discusses how vectors and matrices are used in robotics to represent 2D and 3D positions, directions, rigid body motion, and coordinate transformations. It is assumed that all students will have taken a course in linear algebra and can refresh themselves on basic definitions.
Dr Nicolas Holzschuch. University of Cape Town. e-mail: holzschu@cs.uct.ac.za. Map of the lecture. • Transformations in 2D: – vector/matrix notation – example: translation, scaling, rotation. • Homogeneous coordinates: – consistant notation – several other good points (later) • Composition of transformations • Transformations for the window system.
Coordinate transformation: x = cos sin. sin cos. Take the inverse: y0 x0 = cos sin. sin cos. y0 = r sin. = r sin( + )
