- #1
ASmc2
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This is a question to those who have the 3rd edition at their disposal. Where do 3.45 and 3.46 come from? I understood everything he said before that...
Where Do Sections 3.45 and 3.46 in Goldstein's 3rd Edition Originate?
- Thread starter ASmc2
- Start date
In summary, there is a discussion about equations in the 3rd edition of a book. The conversation focuses on deriving equations 3.45 and 3.46 through linearization and simple harmonic motion. There is a mention of a mistake in the first equation and the correct equation is obtained with the help of someone else.
- #2
voko
- 6,054
- 391
Start with equ. 3.34, an linearize it about ##u = u_0##. You will get an equation for simple harmonic motion, from which those two equations will follow.
- #3
ASmc2
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I get an equation of the form x''+kx=c. where c is some constant, '' gives the second derivative with respect to theta, and x is u-u0.
- #4
voko
- 6,054
- 391
You are on the right track, but you should have obtained ##x'' + kx = 0##. You made a mistake somewhere. Without seeing your work, I can't say what it was.
- #5
- #6
ASmc2
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That u0^3 and u0 terms bother me, as you can see.
- #7
voko
- 6,054
- 391
The very first equation you have is incorrect. $$ {d \over du} V \left( \frac 1 u \right) \ne f(u) $$ Which is actually strange, because the third equation could only have been obtained if you had differentiated that correctly.
- #8
ASmc2
- 28
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OK, I get that now, thanks. I got the correct equation now. Now to get (3.46).
- #9
voko
- 6,054
- 391
3.46 should follow from what you got immediately: ##\ddot x + \beta^2 x = 0 ##.
- #10
ASmc2
- 28
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Yes. Thanks for the help with 3.45
Related to Where Do Sections 3.45 and 3.46 in Goldstein's 3rd Edition Originate?
1. What is the main topic of Godstein Chapter 3?
The main topic of Godstein Chapter 3 is the theory of relativity and its implications for the understanding of space and time.
2. What are some key concepts covered in Godstein Chapter 3?
Some key concepts covered in Godstein Chapter 3 include the principle of relativity, the speed of light, and the equivalence of mass and energy.
3. How does Godstein Chapter 3 relate to other chapters in the book?
Godstein Chapter 3 builds upon the concepts introduced in previous chapters, such as the laws of motion and the concept of inertia. It also lays the foundation for future chapters on gravity and cosmology.
4. What are some real-world applications of the theories discussed in Godstein Chapter 3?
The theories discussed in Godstein Chapter 3 have many real-world applications, including the development of GPS technology, nuclear power, and the understanding of the behavior of objects traveling at high speeds.
5. How can I better understand the complex concepts in Godstein Chapter 3?
To better understand the complex concepts in Godstein Chapter 3, it is helpful to read through the chapter multiple times, take notes, and consult additional resources such as online lectures or textbooks. It may also be beneficial to discuss the chapter with a colleague or teacher who can provide further explanations and insights.