Large Amplitude Pendulum Equation

[StevenJacobs990]

The equation for large-angle pendulum can be infinitely long. What is the pattern with the latter numbers in "..."?

 

[sophiecentaur]

Sorry, your attachment won't open for me.

 

[sophiecentaur]

Does this link help?

 

[StevenJacobs990]

Does this link help?

Yeah, but what's the pattern that comes after 11/3072 (theta)^4?

 

[Vanadium 50]

There is no pattern. That's why you need the elliptic integrals.

 

[sophiecentaur]

Yeah, but what's the pattern that comes after 11/3072 (theta)^4?

AS I said before, your attachment is not readable.

 

[StevenJacobs990]

This is the attachment

 

[wolf1728]

Here is a graphic I made.
Look at equation 3.

 

[wolf1728]

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:

 

[rumborak]

Honestly, I wouldn't be surprised if this a Taylor expansion of some sort.

 

[sophiecentaur]

Honestly, I wouldn't be surprised if this a Taylor expansion of some sort.

. . . .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.

 

[wolf1728]

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.