So, lemme see if I've got this straight...
In summary, once the minus sign and some square root symbols are inserted into the graphics, WD Clinger has one basic complaint remaining: The use of viewer coordinate systems.
tfk: "Hey, Major Tom, we agreed that I was going to sell you my pickup truck for $1,000. And now you show up demanding that I give you the truck AND a check for $1,000,000??"
Major Tom: "Ahh, it's just a silly square root symbol. What are you getting all worked up about?"
tfk: "Explain why I should give YOU a check for any amount, when you are buying my truck?"
Major Tom: "Ahhh, it's just a silly minus sign. Just write the check & toss me the keys."
tfk: "Frappe la rue."
In summary, WD explicitly notes 16 errors. You correct two, and think that leaves one more. In other words, in your world 16 - 2 = 1.
inneresting…
Pssst, was the "arctan2π" argument lost on you?
inneresting…
Pssst, you don't stick square root symbols into graphics. You stick 'em into equations.
He recommends only using the "plumb" coordinate system, while I will use multiple coordinate systems for different purposes.
It is pretty easy to see why the building coordinate system is useless to describe motion as it is seen from each viewpoint.
So, there is ONLY ONE coordinate system that is objective & "reality based". That is, is the only coordinate system that easily & clearly tells one what the top block of the tower is really doing in terms of tilting & descending. This is a coordinate system that is tied to the walls & corners of the building itself.
Every other coordinate system is a subjective, 2D projection of that 3D reality based system taken from various viewpoints. In other words, all dimensions & measurements taken from any of those other viewpoints are guaranteed to be wrong, unless perspective & depth are carefully considered.
And the one coordinate system that you disparage & refuse to consider is one tied to the building & to objective reality.
inneresting...
It is impossible to reproduce motion in the building coordinate system by using the Sauret video.
What you really see is movement as it is projected onto the Sauret viewpoint.
DING DING DING DING DING DING DING !!!
WE HAVE A WINNAH!!
Gee, that didn't take too long, did it?
Read it again.
For comprehension.
Think about what it means about the inverse transform. (Sauret coordinates to building coordinates)
The question is: How is rigid tilting seen from the Sauret perspective, and using building coordinates to describe this is a pretty silly thing to do.
The APPARENT rotation & translation of the upper block as viewed from the Sauret video is different from the APPARENT rotation & translation of the upper block as viewed from the CBS video, which is different from the APPARENT rotation & translation of the upper block as viewed from any other perspective. None of those subjective, different, apparent rotations & translations of the upper block matter one iota.
The one and only rotation & translation of the upper block that matters is the REALITY BASED one: the 3D rotation & translation with respect to the planet earth. (i.e., the source of the gravitational field that generates one primary group of forces on all members. And with respect to the supports in the building, the structure that supplies the second primary group of forces in the building. And these forces happen to be pretty darn closely aligned with the walls of the building, prior to the start of the collapse.
And yet, this is the one coordinate system that you disparage & refuse to consider.
inneresting...
In my coordinate systems, mathematics will be quite simple. In yours, a real mess.
I'd really prefer "correct math" to "simple math".
I'd really prefer REAL motion to APPARENT motion.
I'd really prefer a COMPETENT analysis to, well, yours.