[Cleonis]

About d'Alembert's principle. A modern name for it is 'd'Alembert's virtual work'.

The modern concept of 'work done' was formulated around 1850 (Eighteen-fifty). That is, we shouldn't assume that back in the days of Lagrange d'Alembert's principle was understood in the same way as it is today.

Joseph Louis Lagrange motivated his notion of potential energy in terms of d'Alembert's principle.

The recurring theme is the concept of 'work done'.

In case you hadn't noticed yet, I'm the contributor who notified you of a resource I created, with interactive diagrams.

There is this distinction: the work-energy theorem expresses physical motion, whereas d'Alembert's virtual work expresses, as the modern name indicates, virtual work.

My assessment is that using d'Alembert's virtual work is an unnecesarily elaborate approach. The same result can be arrived at in a more direct way.

[in_a_hole]

I haven't had a chance to really dig into your resource yet but I am definitely going to do so. Perhaps I'll wait a few days until the change you mentioned is implemented.