On Wed, Nov 16, 2011 at 10:18 AM, Aaron Meurer <[email protected]> wrote: > On Wed, Nov 16, 2011 at 11:12 AM, Luke <[email protected]> wrote: >> Do you mean in my solution that involves differential equations? > > Yes (assumedly the solution will be the same no matter what method you > use to derive it, so long as you always make the "small angles" > approximation). > >> >> I think this dimensional analysis approach may have merit, I just need >> to see all the steps and make sure they can all be justified without >> referencing a differential equation. >> >> ~Luke > > Perhaps this would be easier to see (at least for someone like me who > doesn't remember this particular part of physics very well) if you > added explicit dimensions to all the numbers in your derivation. It's > hard to tell which "1's" are really unit-ed. > > And by the way, I'm still convinced that the "trick" involves deriving > it geometrically somehow, although in my experience, dimensional > analysis is a favorite among the types who like to use little tricks > to derive things.
Anyway, thanks Luke for bringing this in! I am positive we can nail this out, or somebody will eventually. In fact, I consider the whole high school physics full of such "tricks". That's why I hated physics back then. Now after lots of years when I can see that one can actually derive everything very systematically using an engineering approach, I actually love physics. So I consider myself more of an engineer than a physicist. But I must say, that after I understand the problem from a systematic engineering perspective, I greatly enjoy these "physical", tricky arguments. In fact, I have great fun deriving all the "tricky" formulas (like currents/forces between wires...) in electromagnetism from a simple classical relativistic formulation, more here: http://theoretical-physics.net/dev/src/elmag/elmag.html the initial section is still a little complex, but I will simplify it over time as I understand things more. Once I understand this example well, I'll put it into this section: http://theoretical-physics.net/dev/src/relativity/classical.html I just started this classical mechanics section about two weeks ago, so it's still very crude. I need to figure out how to derive the basic equations needed there from general relativity: http://theoretical-physics.net/dev/src/relativity/relativity.html But it will take some time. I know how to derive the Newton's law from Einstein equations as well as the gravitational law, but I don't see currently how to connect the Lagrangian formulation with general relativistic Lagrangian formulation. Also how to derive rigid body equations, because one cannot have a rigid body in special relativity, so classical mechanics is a hard subject. But for electromagnetism I think I already understand pretty well how all things follow from the simple relativistic formulation. Ondrej -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
