Phil Lucht Math & Physics Archive
Home / Math and Physics Files / Physics / Mechanics / frames doc stuff / Active Passive and Covariance

Active vs Passive in my docs

DOCX · 124.0 KB
Open DOCX file

A short personal note by Phil dated 11.23.16 that sets out to review all his rotation-related documents but does not get far. It links the tensor doc's way of working to covariant equations, where in frame S' an equation keeps the same form with primed quantities (F' = RF, a' = Ra, m' = m). It also mentions Appendix K on deformation tensors and hints that u'n = R-1un might build an active/passive account tied to the tensor doc, which is not carried out. Equations were lost in extraction.

AI-written summary; may contain errors. This description is approximate.

Extracted text (machine-read; may contain errors)
Active vs Passive in my docs PhL 11.23.16 This one page note sets out to review all my rotation-related docs, but does not get far! But I do realize a key thing here which is the strong association between tensor doc's way of doing things and covariant equations. I also get a hint that maybe I can use u'n = R-1un as an equation to construct a version of the active/passive story which relates to tensor doc, but I don't actually do it here. 1. Tensor Doc It includes the following equations, for example I do mention "frames of reference" in several places. A main idea is this one The idea is that in Frame S' a covariant equation "has the same form but everything is primed". In the above example I would write F' = RF and a' = Ra and m' = m, but I don't interpret this beyond implying that the Frame S' person would measure primed quantities. Frame appears a lot in App K about deformation tensors. But below K.5.26 I say this This is the only place that the word "active" appears in tensor doc, and this is my usual active vs passive discussion.