Check out the new HLFF Blog article by Benjamin Skuse, where he examines the calculus of variations.
We have all been in the situation where we cannot get a gadget or device to work. We have tried every button, lever and switch. We have watched every ‘how-to’ YouTube video, and still it will not work. Our last resort? Give it a good old shake. This is the fundamental essence of the calculus of variations: We wiggle a functional (a function of functions) a little bit to be able to identify the stationary values (maxima, minima, saddle points, possibly global or local) of that functional. The calculus of variations is an important field of mathematical analysis, is central to our understanding of reality and the universe and has been applied extensively in the design and development of the essential technologies and products we use today. But few know the story of the calculus of variations.
Check out part 1 of Benjamin Skuse’s deep dive into the topic here: HLFF Blog
Image caption: Speed on different tracks in the gravitational field. The fastest track (red) is a Brachistochrone curve. Image credits: MikeRun (CC-BY-SA-4).