1 / 8

§1.1.4 Affine space (points)

Understand affine space concepts, points vs. vectors, coordinate systems, differential elements, and transformations in physics and math conventions.

munsond
Download Presentation

§1.1.4 Affine space (points)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. §1.1.4Affine space (points) Christopher Crawford PHY 416G 2014-09-05

  2. Outline • Affine space – linear space of pointsPoints vs. vectors – comparison and contrastPosition vectors, displacement, differentialAffine combinations, transformations • Cylindrical and spherical coordinatesCoordinate & component transformationsCoordinate lines and surfacesDifferential line (dl), area (da), volume (dτ) elements

  3. Affine Space – points • Points vs. vectors: coordinates vs. components • Position vector • Operations on Points / Vectors • Point + displacement • Head - tail

  4. Weighted points • Weighted point as a vector • Center of mass • Linear errors • Affine transformation

  5. Summary: Points vs. Vectors • Operations • Affine combination • Basis • N+1 vs. N • Decomposition • Coordinates vs. components • Transformations • Affine vs. linear • Fields / Differential / Integral • Parameterization vs. field (coordinates)

  6. Cylindrical & Spherical coordinates • Coordinate transformation • Physics vs. math convention; singularities • Can you mix coordinate systems? • Component transformation

  7. Cylindrical & Spherical coordinates • Differential elements

  8. Example • Position vector as a field in different coordinates

More Related