MTW Ch7: Choosing Lagrangian for Scalar Potential

Click For Summary
SUMMARY

The discussion centers on the challenges faced by a user, TerryW, while working through Chapter 7 of a text on Lagrangian mechanics, specifically regarding Exercise 7.1 (a). The user questions the rationale behind choosing eφ over φ in the integral for I and seeks guidance on how to approach the problem. Despite completing most exercises in Chapter 6, TerryW expresses frustration over not deriving differential equations and achieving only a trivial result of 0 = 0. The conversation highlights the need for clarity in the application of Lagrangian principles.

PREREQUISITES
  • Understanding of Lagrangian mechanics
  • Familiarity with scalar potentials in physics
  • Basic knowledge of differential equations
  • Experience with mathematical problem-solving techniques
NEXT STEPS
  • Research the significance of choosing eφ in Lagrangian integrals
  • Study the derivation of differential equations from Lagrangian formulations
  • Explore common pitfalls in solving Lagrangian mechanics problems
  • Review advanced techniques in scalar potential theory
USEFUL FOR

Students and educators in physics, particularly those studying Lagrangian mechanics, as well as anyone seeking to deepen their understanding of scalar potentials and their applications in differential equations.

TerryW
Gold Member
Messages
234
Reaction score
22
I have managed to get to the end of Chapter 6 and have done almost all of the exercises (I didn't get anywhere with exercise 5.6 (d) and have seen the Cesarth/TSny exchange and still don't feel I have a satisfactory solution...) but I have hit a bit of a wall with Exercise 7.1 (a).First question is 'Why choose eφ instead of just φ in the integral for I ?'Next question 'Can anyone give me a hint as to how I should be approaching this?'
I've attached my manuscript working which achieves a result of 0 = 0 (well at least it is consistent) but no differential equations.
Regards
TerryW
 

Attachments

Physics news on Phys.org
Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

Similar threads

Graduate Help with Exercise 7.1 - MTW Chapter 6
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Deriving Equation of Motion for Quintessence Scalar Field?
  • · Replies 9 ·
Replies
9
Views
3K
Graduate Renormalizability conditions for a real scalar field in d dimensions
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Electrodynamics: questions about vector and scalar potentials....
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Geometry of Classical Physics in terms of Gauge Theory geometry?
  • · Replies 2 ·
Replies
2
Views
2K
Studying Skipping Chapters in Stewart’s Calculus? (Pearson's Edexcel IAL Background)
  • · Replies 2 ·
Replies
2
Views
1K
Graduate What is the role of Z, W, and photon fields in the Lagrangian density?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Super-radiance of electromagnetic waves
  • · Replies 8 ·
Replies
8
Views
3K
Graduate MOND Theory Primer: Stacy McGaugh's Research Program Explored
  • · Replies 11 ·
Replies
11
Views
5K