Calculating Elliptic Integrals - Ask Experts for Help

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In summary, the conversation discusses the topic of calculating elliptic integrals, specifically in relation to magnetic field in a coil for magnetic particle testing. One person asks for suggestions on textbooks or websites for calculating these integrals, while another person recommends using numerical methods or specific formulas published in a journal. The second person also mentions their own developed formulas and computer codes for more accurate results.
  • #1
cataldo
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Hi everybody.
I have a simple question for experts of the forum. I must calculate a elliptic integral.. I do not found on my texbooks how calculate it..
Can suggest me some texbooks or internet sites where i must see their calculate?...I have need to have informations on theory and exercise...
Best regards
Aldo
 
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  • #2
Elliptic integrals in general can't be calculated analytically, by finding an anti-derivative, and require a numerical integration, say by Simpson's rule.

When I was in college, I remember seeing a bookcase in the college library holding forty volumes of nothing but values of Elliptic integrals for various values of the parameters!
 
  • #3
Hi hallsofIvy...
Tanks for your replay...
I know that elliptic integrals can be calculated with numerical methods and never analytically... but i have need some titles of the textbooks on elliptic intgrals...I must calculated an elliptic integral on magnetic field in coil for magetic particle testing...
 
  • #4
If your coils are extremely thin, you can use the analytic formulas published by Milan Wayne Garrett in 1963 in the Journal of Applied Physics. (These formulas use Elliptic Integrals of all three kinds. You can evaluate these elliptic integrals using Carlson's algorithms.) If your coils are *not* extremely thin, I have developed formulas and computer codes that are accurate to one part ber billion, or better, even inside the coils.
 
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Related to Calculating Elliptic Integrals - Ask Experts for Help

1. How do you calculate elliptic integrals?

Elliptic integrals can be calculated using various methods such as power series expansions, numerical methods, and computer algorithms. The most commonly used method is the use of special functions called elliptic functions, which can be evaluated using tables or software programs.

2. What is the purpose of calculating elliptic integrals?

Elliptic integrals have many applications in physics, engineering, and mathematics. They are used to solve various problems involving shapes such as ellipses, spheres, and toroids, and also play a crucial role in the study of celestial mechanics and quantum mechanics.

3. What are the different types of elliptic integrals?

There are three types of elliptic integrals: incomplete, complete, and multiple. Incomplete elliptic integrals have a limited range of integration, while complete elliptic integrals cover the entire range. Multiple elliptic integrals involve multiple variables and have a wider range of applications.

4. How do you simplify elliptic integrals?

Elliptic integrals can be simplified using various methods such as substitution, integration by parts, and trigonometric identities. In some cases, special functions such as the Jacobi elliptic function or the Weierstrass elliptic function can be used to simplify the integral.

5. What are some real-world applications of elliptic integrals?

Elliptic integrals have various practical applications, including calculating the period of a pendulum, solving problems in mechanics and electricity, and determining the shape of planetary orbits. They are also used in cryptography and signal processing, and have applications in fields such as computer graphics and image processing.

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