|
|
Post by Admin on Sept 19, 2023 6:56:40 GMT
Mondo
You don't need to remember, just use the index to the book. That's what it is there for.
Vasco
|
|
|
|
Post by mondo on Sept 19, 2023 8:19:05 GMT
He is talking about the construction outlined in points (i)-(iii) from previous page 545 versus the mapping on figure [25] p542. I more or less understand but the confusion comes from the fact that in the mapping for figure [25] there is no dipole involved, so comparing dipoles placement is misleading. However I think author assumes that no dipole means a dipole is at infinity. Therefore a mapping of dipoles is $\infty$ to $\infty$.
Something I don't get here - author says that placing one of the dipoles at some point outside $R$ allows us to map it to $\infty$ - it makes sense but how is that giving us "missing two degrees of freedom"?
|
|
|
|
Post by mondo on Sept 19, 2023 8:49:12 GMT
Mondo You don't need to remember, just use the index to the book. That's what it is there for. Vasco Also, this is a good suggestion but index is no always complete, take "vortex" as an example - according to index we have it at page 488 only. |
|
|
|
Post by Admin on Sept 19, 2023 9:38:56 GMT
Mondo
You are right.
However in this case it worked out well, I looked up dipole and then -at infinity which directed me to page 492. I then read subsection 9 which gives useful links to other pages.
Vasco
|
|
|
|
Post by Admin on Sept 19, 2023 11:15:39 GMT
He is talking about the construction outlined in points (i)-(iii) from previous page 545 versus the mapping on figure [25] p542. I more or less understand but the confusion comes from the fact that in the mapping for figure [25] there is no dipole involved, so comparing dipoles placement is misleading. However I think author assumes that no dipole means a dipole is at infinity. Therefore a mapping of dipoles is $\infty$ to $\infty$. Something I don't get here - author says that placing one of the dipoles at some point outside $R$ allows us to map it to $\infty$ - it makes sense but how is that giving us "missing two degrees of freedom"? Mondo There is a dipole in figure 25. We have a uniform flow into which we place a dipole at the origin. Also the uniform flow is a dipole at infinity. He means that 2 degrees of freedom seem to be missing (not available) and then explains this by saying that he unnecessarily put another dipole at infinity which subtracted 2 degrees of freedom. So if we get rid of the extra dipole at infinity we can then put a dipole outside $R$ which will then take up these two degrees of freedom. Vasco |
|
|
|
Post by mondo on Sept 20, 2023 8:03:36 GMT
Vasco, yes but the question is why do we have to use these dipoles to add two degrees of freedom? Why not use some combination of points?
Also, why an addition of a dipole results in two degrees of freedom and not just one?
|
|
