I'm trying something new today. I've been doing some background reading on the supposed violation of special relativity reported by M Mansuripur in PRL and pointed out by +Cliff Harvey earlier this week. The embedded document below is a linked diagram of the background articles I've been reading. An arrow indicates that the article referenced the pointed at article. My goal in reading about this was to learn about the 'hidden momentum' issue mentioned in Mansuripur's article. The articles listed here are the earliest and, in my opinion, the most basic articles I could find on the subject.
Now available as a Kindle ebook for 99 cents ! Get a spiffy ebook, and fund more physics The following is a pretty lengthy procedure, but converting the divergence, (nabla, del) operator between coordinate systems comes up pretty often. While there are tables for converting between common coordinate systems , there seem to be fewer explanations of the procedure for deriving the conversion, so here goes! What do we actually want? To convert the Cartesian nabla to the nabla for another coordinate system, say… cylindrical coordinates. What we’ll need: 1. The Cartesian Nabla: 2. A set of equations relating the Cartesian coordinates to cylindrical coordinates: 3. A set of equations relating the Cartesian basis vectors to the basis vectors of the new coordinate system: How to do it: Use the chain rule for differentiation to convert the derivatives with respect to the Cartesian variables to derivatives with respect to the cylindrical variables. The chain ...
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