There is a special toolkit, sympy.physics.mechanics (and for beam bending specifically, the new sympy.physics.continuum_mechanics).
This trick seems mostly harmless, since SymPy treats DiracDelta outside of integration symbolically (i.e., DiracDelta(x) = 0 if x != 0 and oo if x = 0). As I noted before, by that symbolic definition (a function that is 0 except at a single point), the limit is 0, so things work out. The problem with treating something like DiracDelta like a normal expression is that you can't just put it anywhere in an expression and expect it to make sense (what is sin(DiracDelta(x))?). But for a specialised mechanics toolkit, it is only going to create expressions that make physical sense (and hence, mathematical sense with the "shaky" definitions). Aaron Meurer On Sun, Aug 14, 2016 at 9:58 AM, Richard Fateman <fate...@gmail.com> wrote: > I am not familiar with this trick, but just because engineers > in some area hack together some method that is mathematically > dubious, doesn't mean it should be introduced as a default in sympy. > (Maybe it should, maybe it is harmless?) An example that > also involves context that sympy would not know about is > how to deal with certain expressions involving infinity. E.g. > is 0*oo equal to 0 or "indeterminate" ? what about oo = oo ? > > One way of looking at this may be to build some "mechanics" > toolkit with such tricks. > > RJF > > > On Sunday, August 14, 2016 at 3:12:29 AM UTC-7, SAMPAD SAHA wrote: >> >> >> In Mechanics, while solving beam bending problems, we need to find out >> the reaction force at first. There is a trick I have learned from Jason. >> Suppose there is beam of length l, then we at first find the load >> distribution using variables multiplied by dirac deltas in place of >> reaction forces. After finding shear force curve and bending moment curve >> in terms of those variables, we equates them to 0 for x = l+ >> >> Now for tthis case we have to use the limit. >> >> Regards >> Sampad Kumar Saha >> Mathematics and Computing >> I.I.T. Kharagpur >> >> On Sun, Aug 14, 2016 at 12:27 PM, Aaron Meurer <asme...@gmail.com> wrote: >> >>> I agree that DiracDelta doesn't make sense except under an integral >>> sign. But as a function that is 0 everywhere except for one point, in a >>> limit, it can be replaced with 0, which is what SymPy's limit() appears to >>> be doing. I am curious how you are ending up with an expression with a >>> DiracDelta that you need to take a limit of, though. >>> >>> Aaron Meurer >>> >>> On Sat, Aug 13, 2016 at 8:34 PM, Richard Fateman <fat...@gmail.com> >>> wrote: >>> >>>> Since DiracDelta is a distribution, not a function, and presumably the >>>> limit program is oriented toward finding limits of analytic functions, >>>> it would be fairly reasonable for the limit program to not work on >>>> this kind of expression. The mathematical context in which DiracDelta >>>> is >>>> understood and useful is under an integral sign. >>>> >>>> I have not tried sympy on this example, but it seems to me >>>> that expecting sympy to answer a poorly formulated question >>>> "correctly" is not going to reveal a bug in the program. It >>>> is "user error". >>>> >>>> RJF >>>> >>>> >>>> On Saturday, August 13, 2016 at 5:25:22 AM UTC-7, SAMPAD SAHA wrote: >>>>> >>>>> Suppose I want to find the value of f(x) for >>>>> f(x) = DiracDelta(x - 30) + Heaviside(x) at x = 30+ in sympy. How can >>>>> we do this? >>>>> >>>>> Regards >>>>> Sampad Kumar Saha >>>>> Mathematics and Computing >>>>> I.I.T. Kharagpur >>>>> >>>>> >>>>> >>>>> >>> -- >>> You received this message because you are subscribed to the Google >>> Groups "sympy" group. >>> To unsubscribe from this group and stop receiving emails from it, send >>> an email to sympy+un...@googlegroups.com. >>> To post to this group, send email to sy...@googlegroups.com. >>> Visit this group at https://groups.google.com/group/sympy. >>> To view this discussion on the web visit https://groups.google.com/d/ms >>> gid/sympy/CAKgW%3D6JAO7i1f-X6uw-WiiztsV%3DXh2Tt74crv3ULhFKr1 >>> oz2Bg%40mail.gmail.com >>> <https://groups.google.com/d/msgid/sympy/CAKgW%3D6JAO7i1f-X6uw-WiiztsV%3DXh2Tt74crv3ULhFKr1oz2Bg%40mail.gmail.com?utm_medium=email&utm_source=footer> >>> . >>> >>> For more options, visit https://groups.google.com/d/optout. >>> >> >> -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sympy+unsubscr...@googlegroups.com. > To post to this group, send email to sympy@googlegroups.com. > Visit this group at https://groups.google.com/group/sympy. > To view this discussion on the web visit https://groups.google.com/d/ > msgid/sympy/1ca3f3e9-4f9b-4cea-bdcb-5d62f3e8ee44%40googlegroups.com > <https://groups.google.com/d/msgid/sympy/1ca3f3e9-4f9b-4cea-bdcb-5d62f3e8ee44%40googlegroups.com?utm_medium=email&utm_source=footer> > . > > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To post to this group, send email to sympy@googlegroups.com. Visit this group at https://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAKgW%3D6%2BPJkJcu5ZYKixsm7ffS4OrgmgmiXnMA50zKSjZ1RXihw%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
