the pendulum hit also has a musical purpose. he's trying to hit the two cymbals of different notes with the right hand because he's maintaining a sort of metronome effect. he can not use his left hand because his left hand will be used to hit some cymbals and toms in his left hand side while he is doing the metronome.
Nah. Left hand isn't doing anything when he first starts doing the pendulum thing. Its just a showmanship thing, nothing more. He could just as easily play the same ride cymbal for the four measures rather than switching between the two different rides - he's doing it because he thinks it looks cool.
There is showmanship there, but the two rides are different and they produce different sounds. The first four measures, his left hand indeed was not doing anything, but it does two crash hits later, while his right hand was still doing the metronome. And while you may not notice much difference, that really is just the way MM is very anal about his use of cymbals. He also does the same thing in the intro and the outro of Illumination Theory, where he he shifts to different cymbals based on pitch.
He gave a very good interview once on how he plays cymbals in songs.
https://www.metalsucks.net/2011/09/29/rigged-dream-theater%E2%80%99s-mike-mangini-takes-you-through-every-piece-of-his-mega-drumkit-part-2/"I have two ride cymbals. On my far left is a tight earth ride (a real thick, heavy thing) and on my right side it’s a Zildjian 20″ A Custom cymbal which is a more open sound. It’s a very airy sound, not so much Alex Van Halen or John Bonham openness, but it definitely has more ring to it. I’ll choose one of those ride sources based on how much tightness or openness I want for the ride cymbal. That is kind of the way I choose an open hi-hat vs. a closed hi-hat."
"Again, and to reiterate this, all the metal on my kit is a frequency based thing to match the music."