StevenJacobs990
- 16
- 0
The equation for large-angle pendulum can be infinitely long. What is the pattern with the latter numbers in "..."?
Large Amplitude Pendulum Equation
Join the discussion
Ask a follow-up here, or get your own question answered by working scientists, mathematicians and engineers — people, not an autocomplete.
Real named experts · corrections over time · the nuance an AI answer skips
11 replies · 7K views
- 30,547
- 7,530
Sorry, your attachment won't open for me.
- 30,547
- 7,530
StevenJacobs990
- 16
- 0
Yeah, but what's the pattern that comes after 11/3072 (theta)^4?sophiecentaur said:
- 35,014
- 21,722
There is no pattern. That's why you need the elliptic integrals.
- 30,547
- 7,530
AS I said before, your attachment is not readable.StevenJacobs990 said:
StevenJacobs990
- 16
- 0
This is the attachment
wolf1728
Gold Member
- 38
- 5
Here is a graphic I made.
Look at equation 3.
Look at equation 3.
wolf1728
Gold Member
- 38
- 5
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
- 706
- 154
Honestly, I wouldn't be surprised if this a Taylor expansion of some sort.
- 30,547
- 7,530
. . . .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.rumborak said:
wolf1728
Gold Member
- 38
- 5
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.
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.