Ellipsoid surface area
08-05-2022, 04:51 PM
Post: #6
 Albert Chan Senior Member Posts: 2,100 Joined: Jul 2018
RE: Ellipsoid surface area
Example: Elliptic Integral of the First Kind (note: we use elliptic parameter m=k^2)

>>> from mpmath import *
>>> ellipf(2,3)
1.0010773804561062-1.490278044744527j

RFD(x,y,z) can do both (F, E) at the same time.
Code:
FE(t,m) := // return [F(t,m), E(t,m)-F(t,m)] BEGIN t := sin(t); m *= t*t; return RFD(1-t*t,1-m,1) .* [t, -m*t/3]; END;

Formula is good for angle = 0 .. pi/2

CAS> k := FE(pi/2,3)[1]      → 1.00107738046-1.17142008415*i

// 2 = 2*pi/2 + (2-pi)
CAS> 2*k + FE(2-pi,3)[1]                             → 1.00107738046-1.49027804474*i

// 2 = pi/2 + (2-pi/2)
CAS> k + FE(2-pi/2,3/(3-1))[1]/sqrt(1-3)      → 1.00107738046-1.49027804474*i
 « Next Oldest | Next Newest »

 Messages In This Thread Ellipsoid surface area - Albert Chan - 05-28-2021, 12:37 AM RE: Ellipsoid surface area - Albert Chan - 05-28-2021, 08:05 PM RE: Ellipsoid surface area - Albert Chan - 05-30-2021, 06:04 PM RE: Ellipsoid surface area - Albert Chan - 05-31-2021, 01:38 AM RE: Ellipsoid surface area - Albert Chan - 08-05-2022, 04:40 PM RE: Ellipsoid surface area - Albert Chan - 08-05-2022 04:51 PM

User(s) browsing this thread: 1 Guest(s)