Tey don't do anything. Check some quantum mechanics maybe an electric field strong enough over a neutron can split it into more fundamental particles with charge different than zero
Red shift:
http://www.tubepolis.com/play.php?q=red%20shift&title=The%2Bdoppler%2Beffect%2Band%2Bred%2Bshift-a%2Bbeginners%2Bguide&id=Man9ulEYSgk&img=http%253A%252F%252Fi.ytimg.com%252Fvi%252FMan9ulEYSgk%252Fdefault.jpg
Calculate its rotational of the vectorial function, if its zero then try calculating the singularities inside C(where the function is infinite) Then isolate the singularities with circles with radius h with h going to zero. Evaluate the line integrals of those circles and there is your awnser...
Ask the experts: nice video explaining the center of the universe
http://www.tubepolis.com/play.php?q=universe%20has%20a%20center&title=The%2BUniverse%2BHas%2BNo%2BCenter...%2Band%2BYoure%2BNot%2BThere&engine=1&id=9kjvXkoDCJ0&img=http%253A%252F%252Fi.ytimg.com%252Fvi%252F9kjvXkoDCJ0%252Fdefault.jpg
Jajaja check this docu about barbershops:
http://www.tubepolis.com/play.php?q=barbershops&title=Barbershops%3A%2BUncut&id=kBw8uS1OjSw&img=http%253A%252F%252Fs4.ytimg.com%252Fvi%252FkBw8uS1OjSw%252Fdefault.jpg
try calculationg a really simple integral to test your program. If that works it's probably an error of the machine. Try placing instead of real integers like 4 use 4.0.
Also try placing prints along the program to see if everything is working ok.
If that doesn't work try this other simpson...
Check this to understand the center of mass better:
http://www.tubepolis.com/play.php?q=center%20of%20mass&title=Center%2Bof%2BMass%2C%2BConservation%2Bof%2BLinear%2BMomentum%2BPart%2B1&engine=1&id=ROYYNJkhG4g&img=http%253A%252F%252Fi.ytimg.com%252Fvi%252FROYYNJkhG4g%252Fdefault.jpg
Natural sciences are not really sciences in the strict way of what science objectives are. (Read Karl popper). But humanities and sciences of course are connected.
Easy. The particles in the edge of ball are rotating. At angular speed C*R (Hoping R<1 because if not Einstein gets mad). Then the contraction it's in the direction of the velocity (whicks keeps changin beacuse of the rotation). Then there's another movement seen form the center of the mass also...
I think you're right. You seem to have done everything ok. Just try to simplifiy both result solving the Newton binomials. Probably everything will reduce and you'll have your right awnser.
Remember if you get tired check the trigger happy videos at tubepolis.com They're really really funny...