Sojourner01 said:
Hmph, Dewar's work is fine right up until halfway down page 4. Like most other books I've seen, there's no explanation whatsoever of why the definitions given are the case.
"The condition for functional independence of the m constraints is that the rank of the matrix [whatever] must be its maximal possible value, m."
Why? If I knew the mathematics so well, I wouldn't need this book, would I?
I agree that Dewar's notes might be a little advanced...which might be expected of something concise. However, to be fair, the complete quote is:
"The condition for functional independence of the m constraints is that
there be m nontrivial solutions of eq. (1.3), i.e. that the rank of the matrix
\partial f_j({\mathbf q})/\partial q_i be its maximal possible value, m."
where eq. (1.3) was
\sum_{i=1}^n \displaystyle\frac{\partial f_j({\mathbf q})}{\partial q_i} {\rm d}q_i \equiv \displaystyle\frac{\partial f_j({\mathbf q})}{\partial {\mathbf q}} {\rm d}{\mathbf q} =0
The use of the term rank was to help restate the main sentence with a little more mathematics. On a first or second pass, one could gloss over those finer mathematical details.
The Woodhouse text might be a little more your speed.
In it, he addresses what he has dubbed as the first and second "fundamental
confusions of calculus".
Doughty's text also treats the more advanced "Lagrangian field theory", which you used in the title of this thread.
For something online, you might like:
Richard Fitzpatrick's Analytical Classical Dynamics: An intermediate level course
http://farside.ph.utexas.edu/teaching/336k/336k.html
