Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
It is convenient to write 2(o) in the form z = ² sin² p, use the fact that 2'(x) = 2'(o)/x'(o) and express the integrand of the functional in terms of o: But 2' Т T-S" do = da do 1+2' (0)²/x' (0)² 2gz (6) 2c² sin o cos o and, since x = x2 +2¹2 = 4c² sin² and = T: = To dov 0 ² (20 - sin 2) + d, a' = 2c² sin² p, so that 2c 2cob T= √29 Jo do= √2g But, from the analysis preceding the exercise, c= √A/sin, and so x¹ (0)² + 2¹(0)² z (0) 2 2А ФЫ g sin o

It is convenient to write 2(o) in the form z = ² sin² p, use the fact that 2'(x) = 2'(o)/x'(o) and express the integrand of the functional in terms of o: But 2' Т T-S" do = da do 1+2' (0)²/x' (0)² 2gz (6) 2c² sin o cos o and, since x = x2 +2¹2 = 4c² sin² and = T: = To dov 0 ² (20 - sin 2) + d, a' = 2c² sin² p, so that 2c 2cob T= √29 Jo do= √2g But, from the analysis preceding the exercise, c= √A/sin, and so x¹ (0)² + 2¹(0)² z (0) 2 2А ФЫ g sin o

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

Can you work out more details, I don't understand.

Solution to Exercise 5.7 It is convenient to write z(p) in the form z = c² sin²o, use the fact that z'(x) = z'(o)/x'(o) and express the integrand of the functional in terms of o: T = 5.² 0 = do dx do 1+2'(o)²/x' (0)² 2gz (6) = T = 32 10th T= But z' = 2c² sino cos and, since x = =²(26 – sin 26) + d, a' = 2c² sin² 6, so that x¹² +2¹² = 4c4 sin² and 2c 2cob √29 16th /2g √2g But, from the analysis preceding the exercise, c = √Ã/ sino, and so do = do 2A b x'(0)² + 2¹(0)² z (0) g sin ob
Transcribed Image Text:Solution to Exercise 5.7 It is convenient to write z(p) in the form z = c² sin²o, use the fact that z'(x) = z'(o)/x'(o) and express the integrand of the functional in terms of o: T = 5.² 0 = do dx do 1+2'(o)²/x' (0)² 2gz (6) = T = 32 10th T= But z' = 2c² sino cos and, since x = =²(26 – sin 26) + d, a' = 2c² sin² 6, so that x¹² +2¹² = 4c4 sin² and 2c 2cob √29 16th /2g √2g But, from the analysis preceding the exercise, c = √Ã/ sino, and so do = do 2A b x'(0)² + 2¹(0)² z (0) g sin ob
Now substitute z = c² sin² to give x = 2c² [dósin² 6 = c² I do ² (26-sin 20)+d and stationary path the time of passage is = do (1 - cos 26) z = T[z] = - ² (1 — cos 26), 2A ob g sin ob to show that on the
Transcribed Image Text:Now substitute z = c² sin² to give x = 2c² [dósin² 6 = c² I do ² (26-sin 20)+d and stationary path the time of passage is = do (1 - cos 26) z = T[z] = - ² (1 — cos 26), 2A ob g sin ob to show that on the
Expert Solution
steps

Step by step

Solved in 4 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS