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B Large Amplitude Pendulum Equation

  1. Sep 17, 2016 #1
    The equation for large-angle pendulum can be infinitely long. What is the pattern with the latter numbers in "..."?



    pendl3.gif
     
  2. jcsd
  3. Sep 17, 2016 #2

    sophiecentaur

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    Sorry, your attachment won't open for me.
     
  4. Sep 17, 2016 #3

    sophiecentaur

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    Does this link help?
     
  5. Sep 18, 2016 #4
    Yeah, but whats the pattern that comes after 11/3072 (theta)^4?
     
  6. Sep 18, 2016 #5

    Vanadium 50

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    There is no pattern. That's why you need the elliptic integrals.
     
  7. Sep 18, 2016 #6

    sophiecentaur

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    AS I said before, your attachment is not readable.
     
  8. Sep 19, 2016 #7
    This is the attachment

    pendl3.gif
     
  9. Oct 10, 2016 #8
    Here is a graphic I made.
    Look at equation 3.
    pendulum.png
     
  10. Oct 18, 2016 #9
    pendulum.png StevenJacobs990
    I don't know the equation for generating those numbers in the formula but here is the large amplitude formula carried out to theta 20:
     
  11. Oct 18, 2016 #10
    Honestly, I wouldn't be surprised if this a Taylor expansion of some sort.
     
  12. Oct 19, 2016 #11

    sophiecentaur

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    . . . .or something else. There are (my Mathematician friends tell me) many equations that can only be solved using a series - Taylor or not so well known ones.
     
  13. Oct 20, 2016 #12
    I originally was writing a pendulum calculator and while researching the Internet, I came across this topic. Anyway, I finished the calculator and it is online: http://www.1728.org/pendulum.htm
    It can calculate pendulum periods up to theta 14 and uses the arithmetic mean to calculate exact pendulum periods.
    Try it out if you like.
     
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