[ODE] Re: Combining contact surface parameters

[Alex Rubinsteyn]

>Is there any realistic justification in either case for/against
>sqrt(A*B) rather than simply (A*B)? 

Check out common coefficients of sliding friction: 
http://www.roymech.co.uk/Useful_Tables/Tribology/co_of_frict.htm

Cast Iron on Cast Iron: 0.15
Oak on Oak (cross grain): 0.32
Cast Iron on Oak: 0.49

0.15 * 0.32 = 0.048
sqrt(0.15) * sqrt(0.32) = .219
(0.15 + 0.32) / 2 = .235

None are accurate, but mean (A,B) is closest (not by much) 
=====================================

Cast Iron on Cast Iron (greasy):  0.07
Cast Iron on Oak (greasy):  0.075
Oak on Oak (greasy, cross grain): 0.072

0.07 * 0.075 = 0.00525
sqrt(0.07) * sqrt(0.075) = 0.075
(0.07 + 0.075) = 0.0725

mean(A,B) and sqrt(A*B) tie
========================

Glass on Glass: 0.4
Nickel on Nickel: 0.53
Glass on Nickel: 0.56

0.4 * 0.53 = 0.212
sqrt(0.4) * sqrt(0.53) = .46
(0.4 + 0.53) / 2 = .465

Again mean(A,B) is closest (though not by much)
===============================

Steel (Mild) on Steel (Mild): 0.57
Aluminum on Aluminum: 1.4
Aluminum on Mild Steel: 0.47

0.57 * 1.4 = 0.798
sqrt(0.57) * sqrt(1.4) = 0.893
(0.57 + 1.4) / 2 = 0.985

The huge inaccuracy of this fake friction parameter really shows here, nothing is 
very close, A*B comes closest. 
==============================

Even ignoring that A*B has the undesired property of N*N != N, it doesn't do 
very well in modeling the friction coefficients between two different materials. 

mean(A,B) and sqrt(A*B) both do fine with the materials I picked. I wouldn't use 
mean(A,B) because it fails in the case of mu1=1.0, mu2=0.0...where you would 
expect no friction, but instead get mu=0.5

So sqrt(A*B) seems like the best choice