Major_Tom wrote:How did that other guy get g/2?
In the big picture, he got g/2 by starting with a different equation of motion. I'm making a big deal of the asymptotic acceleration but that really falls out of the difference in the way the governing equations are formulated. I assume the g/2 figure is correct as determined by the analysis, the issue is how the analysis differs. Seffen goes into great detail on this, so it's not a big secret; he even has comparison graphs with the method indicating g/3 (though doesn't specifically mention that figure).
I've seized on these acceleration limits because they are easy signposts. I could even accept a host of different variations in initial behavior, but I'd expect simple momentum-only acceleration in the limit to agree no matter the method.
- Bazant says g/3
- the simple derivation of the OP (Cherapanov/shagster/me/etc?) says g/3
- a physics engine says g/3
- Greeningesque discrete algebraic model agrees with physics engine
- simple FEM program agrees (pretty well) with physics engine
The last two need to be checked specifically for g/3, but mutual agreement strongly suggests that's what will be shown. Only Seffen comes out differently, and he makes a point of the difference and why his way is correct.
If he's completely correct, then this would reveal a fundamental flaw in ANY solution framework which is conventionally Newtonian, as evidenced by results above in both the analytical and computational domains. That's hugely important, especially for simulations. 10% error?!?!
If he's correct about the formulation but wrong about the applicability, it's a big problem for his paper (only), which makes this 'improved' technique a centerpiece.
If he's wrong altogether, it's a huge blow for this relatively new spin in engineering mechanics. It would be an important refutation.
Right now, his derivation blisters my eyes. I've tried to follow it with various success many times. I understand what he's doing but there's an awful lot of manipulation and tidying between numbered equations. At the end, I just have to say "yeah" because I haven't comprehended every step. At some point, I'm going to set the problem up in Maxima and let it handle the symbolic math manipulation. I also have to go back to the cited work with Pesce. I did this once before and totally forgot, that's how unremarkable it was.