Exercise 6.7 (E) Show that in polar coordinates the functional .b S[y] = ["ª da √x² + y² √1+y'(x)² becomes S[r] = a and that the resulting Euler-Lagrange equation is d²r 3/dr d0² r do Hence show that equations for the stationary paths are 2 - 2r=0 which can be written as 1 p2 where A and B are constants and 0 ≤ 0< π. = cOb d² d0² do r√r² + r¹(0)² (4)+ - 0. /1 A cos 20+ B sin 20 or A (x² - y²) + 2Bxy = 1,
Exercise 6.7 (E) Show that in polar coordinates the functional .b S[y] = ["ª da √x² + y² √1+y'(x)² becomes S[r] = a and that the resulting Euler-Lagrange equation is d²r 3/dr d0² r do Hence show that equations for the stationary paths are 2 - 2r=0 which can be written as 1 p2 where A and B are constants and 0 ≤ 0< π. = cOb d² d0² do r√r² + r¹(0)² (4)+ - 0. /1 A cos 20+ B sin 20 or A (x² - y²) + 2Bxy = 1,
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
![Exercise 6.7 (E) Show that in polar coordinates the functional
·b
S[y] = [" da √/x² + y² √/1+y'(a)²_becomes_S[r] = " de r
Va
and that the resulting Euler-Lagrange equation is
3 dr
d²r
d0² r de
Hence show that equations for the stationary paths are
2
- 2r=0 which can be written as
d²
d0²
r² + r² (0)²
(-) + - 0.
=
1
= A cos 20+ B sin 20 or A (x²- y²) + 2Bxy = 1,
p2
where A and B are constants and 0 ≤ 0 < π.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F59d44c96-efb1-4f3c-83b3-5a6a84cf94cb%2Fc9d1baf6-2eb4-4b35-81c7-7b09bf0e7b27%2Frk2cvz8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Exercise 6.7 (E) Show that in polar coordinates the functional
·b
S[y] = [" da √/x² + y² √/1+y'(a)²_becomes_S[r] = " de r
Va
and that the resulting Euler-Lagrange equation is
3 dr
d²r
d0² r de
Hence show that equations for the stationary paths are
2
- 2r=0 which can be written as
d²
d0²
r² + r² (0)²
(-) + - 0.
=
1
= A cos 20+ B sin 20 or A (x²- y²) + 2Bxy = 1,
p2
where A and B are constants and 0 ≤ 0 < π.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 5 steps with 14 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
