Yes torquil is correct in the most general sense. My explanation only works if r is a function of qi. Typically, r has many variables, so you need to sum over all of them. In my case, r just had one.
Its all about the inertial reference frames. Remember, Newton's first law, which says you can only apply his laws IFF you are in an inertial reference frame. Centrifugal force comes about if you are in a non-inertial reference frame (like a rotating disk), and is required to explain the motion...
Quick answer: Yes
While you can study and understand the simplistic methods of all Physics without any math, even Newton's laws require at LEAST a GOOD knowledge of single variable calculus, trigonometry, and algebra. Anything more advanced likely requires substantial skill in differential...
I ended up working it out, quite simply really. I was getting held up with q dot, as I was treating it as a function of qs instead of strictly t.
Working out the left side using the chain rule you get:
\frac{d}{dt} \left( \frac{\partial \vec{r}}{\partial q_i} \right) \Rightarrow...
Hello.
I am having trouble realizing the following relation holds in Lagrangian Mechanics. It is used frequently in the derivation of the Euler-Lagrange equation but it is never elaborated on fully. I have looked at Goldstein, Hand and Finch, Landau, and Wikipedia and I still can't reason...