MTW Ch7: Choosing Lagrangian for Scalar Potential

In summary, the conversation discusses the progress made in Chapter 6 and the struggles with Exercise 7.1 (a). The first question is about choosing eφ instead of just φ in the integral for I and the second question asks for a hint on how to approach the exercise. The poster also mentions their manuscript, which does not include any differential equations.
  • #1
TerryW
Gold Member
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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

  • MTW Ex 7.1.a.pdf
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  • #2
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?
 

Related to MTW Ch7: Choosing Lagrangian for Scalar Potential

1. What is the purpose of choosing a Lagrangian for a scalar potential?

The Lagrangian is a mathematical function used in classical mechanics to describe the dynamics of a system. Choosing a Lagrangian for a scalar potential allows us to model the behavior of a system with a scalar field, which is a fundamental concept in physics.

2. How is a Lagrangian chosen for a scalar potential?

The Lagrangian is chosen based on the specific system being studied. It is typically constructed by taking into account the relevant physical laws and symmetries of the system, such as conservation of energy and momentum.

3. What are the advantages of using a Lagrangian for a scalar potential?

Using a Lagrangian allows for a more elegant and intuitive approach to solving problems in classical mechanics. It also allows for the use of powerful mathematical techniques, such as the Euler-Lagrange equations, to derive the equations of motion for a system.

4. Can a Lagrangian for a scalar potential be used for any system?

Yes, a Lagrangian can be used for any system that can be described using a scalar potential. This includes a wide range of physical systems, such as particles in a gravitational field or a simple harmonic oscillator.

5. Are there any limitations to using a Lagrangian for a scalar potential?

While the Lagrangian is a powerful tool, it may not always be the most efficient or practical approach for certain systems. In some cases, it may be more useful to use other mathematical methods, such as Hamiltonian mechanics, to describe the dynamics of a system.

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