Dear Greg, In case of Newton's force there should be a *minus sign *in front, since the force is *attractive*. I also checked the first few equations of the electromagnetic case, it looks OK though I haven't checked the equations that come afterwards.
Best wishes, Furkan Semih. On Fri, Jun 5, 2020 at 9:52 PM Gregory Bard <[email protected]> wrote: > Dear Prof Crisman, Prof Coleman, and perhaps Prof Dündar, > > On the specific issue of symbolic manipulation inside of physics formulas, > there's a little bit of risk because I haven't taught a course that uses > that. The last time I took such a course would have been the Summer of 1996 > or 1997. (I'm not certain.) So, it has been a while! :) With that in mind, > would you both please examine these two examples? > > The first is pretty pedestrian, just converting Newton's Inverse-Square > Law of Gravity to polar coordinates. > > > https://sagecell.sagemath.org/?z=eJxNzUsKgzAUheG54B4OdpJYsDRxVHCqu1BsURR8tF5tDaV7bx6CDjK48H8n73JiQYoMfVHpR1ihMDUj5qaay4D7nu9Vr-GKBCmSBFmow9CEF7A1FzhD5UJnJ-hM6kyZTC-E1A7MrtgRasYPM0vcDgpdmiui5U7su-JmzWOkzfz4boQz0hmxGbWZ_Z-jkc7EzsiI2v7ZtbUq6qXr2CGM-R8sr02-&lang=sage&interacts=eJyLjgUAARUAuQ== > > The second considers two electric charges of q_1 Coloumbs, located at (0, > L) and (0, -L). Another charge of q_2 Coulombs is located at (x,y). The > example computes the Coulomb's Law force, again in polar coordinates. Of > course, if rho is fairly large, then this physical arrangement can be > considered equivalent to an electric charge located at the origin, but with > a charge of 2q_1 Coulumbs. I used a Taylor expansion of b=1/rho at b=0 > (i.e. rho=infinity), of the sixth degree, and converted back from b's to > rho's. Accordingly, we get some rho^4 and rho^6 terms, with and without > even powers of either sin(theta) or cos(theta), depending on which simplify > command is chosen. > > <http://goog_873518195> > > https://sagecell.sagemath.org/?z=eJx1kMlugzAURfeR8g9X2cQmlIQxg8Q2q3xDIkiZVAoJhhZU9d9r-6GWVs0Cybx3zvWV36KGLY54uSS4X2z5OegxoMlrtHnSRjghXvD5LAvTrrq2RV2xZbaUg3wyyNVgPkvulY0QR4ShCjRkoKEC12D92cEKbHg68bPD5fHBfqX3Kkzk9TtTiVwHOzJY_VmiiwX76HFQHY1rLZjuyT_5j-OQ45LjjM4wOqKo_nFccjxy3NFR73CAvY6nqEeoT6hnieL1VhbpcEm7smQT0CcwkGDGYq7epY2Gsm6YEn2ryQXjJmITGxMBJmZA5pauCP5egZGEZojdEbsdm8e6t-z_3RwaInhP8O5Bd2iEUHtD7N5K-ltUPf-C5JJ_AcUQqXY=&lang=sage&interacts=eJyLjgUAARUAuQ== > > It might be cool to make a plot of the coordinate plane, and see for which > points this approximation is accurate to within +/-1%. > > Is this the sort of thing that is desirable? Is it too easy? too hard? Is > the physics correct? Perhaps you had something completely different in > mind? Would degree 8 be better? > > I can easily add this as a new section, late in Chapter 4. > ---Greg > > On Friday, May 29, 2020 at 10:51:02 AM UTC-5, kcrisman wrote: >> >> >>> >>> Symbolic manipulation, substitutions, simplification for basic physics >>> formulas. I have done some limited symbolics with Mathematica, but I just >>> had to retire for medical reasons and can't personally justify the cost. I >>> have heard good things about Sage symbolic manipulation capabilities, but >>> so far I have not seen any really good discussion on it, particularly for >>> the newest version. I apparently tried to join the Sage bandwagon right >>> when so many changes took place, and many older code examples just don't >>> seem to work right. If you had a discussion on symbolics it would be a >>> no-brainer to buy your latest edition. >>> >>>> >>>> >> That is true, as a more "advanced" section. See e.g. >> https://math.stackexchange.com/questions/2383818/sagemath-replace-an-expression-in-a-formula-by-a-function-define-previously >> for one of the many widely scattered examples of where to find info on >> doing this well :-( >> > -- > You received this message because you are subscribed to the Google Groups > "sage-edu" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-edu/23c5ae55-7939-4ff3-8aa1-64d7b1d9b06co%40googlegroups.com > <https://groups.google.com/d/msgid/sage-edu/23c5ae55-7939-4ff3-8aa1-64d7b1d9b06co%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- F. Semih Dündar <[email protected]> -- You received this message because you are subscribed to the Google Groups "sage-edu" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-edu/CAODtkKq4S_%3DQEcOgq3tw__twrO1vHr_uMwp3U6SYunujkJ8ukA%40mail.gmail.com.
