[Title correction: My goal was to create images of 2D, 3D, and 4D functionals. I think I missed that target. Instead I have 1D parameterized curves that all move in up to 3D in space + time. I have a clear idea how to write new code that could move independently with two, three, or four parameters. That code is not written now, so I will change the title to more accurately reflect the content.]
Nothing like writing a title where I am not sure if I can pull it off. It reminds me of skiing slowly off a 6 foot cliff in Colorado. By the time I landed, I was going fast. Nothing like the constant acceleration of gravity.
One, Two, Three D
Sophisticated physicists appreciate the dance of abstract symbols. I need to build something. The abstract is more real when made out of clay and pipe cleaners. In this blog on the 1D Euler Lagrange equations, beads (not clay) and pipe cleaners will be used to appreciate this important tool, followed by the same story told with symbols.
[note: I missed my usual self-imposed deadline because I was not able to get the icon bar to appear in Google Chrome on a Mac. The browser Opera worked, so long as I cut and plasted URLs for images and HTML code from codecogs
I spent the week seeing if I could give the good old college try and find a "way that worked" for the gauge games I have been playing. Nothing panned out. Bummer, I had a blog to write. While collecting crumpled paper, there was an old issue I wasn't able to figure out. The answer was probably known a hundred years ago. The blog will explain where I got stuck, and who knows, maybe someone will provide the answer.