Fractional derivatives and suspensions.

[zerodish]

I got interested in suspensions when Dan Henry said tires and bearings last twice as long when you have springs. In the past the fork was designed as a spring. Then mountain bikes came along and they got rid of the spring to make them stronger. Sprung forks have a bit too much dive for me. So I dug into suspension design and discovered it was more like witchcraft than engineering. People would talk with awe about the suspensions of the old Rolls Royce. There is nothing mystical about it. They use a spring that is twice as long and goes all the way up to the top of the hood. It can hit bigger bumps with out bottoming out. Variable rate springs have been tried. They git stiffer the more you compress them. In addition to that automobiles have jounce bumpers which are better than bottoming out on steel. This is fairly straight forward mathematically. An accelerating acceleration is called jerk and an accelerating jerk is called jounce. I think a spring accelerates or deaccelerates a variable rate spring jerks and rubber jounces. But what if you could have suspension which acts between acceleration and jerk or even one that starts out like acceleration then tends toward jerk. Rubber by itself act like this. This is where fractional calculus come in. You can talk about the first and a half derivative. It seems this is now a recognized branch of mathematics and one of their early practical uses is modeling real suspensions. I'm 99 percent practical I came across fractional derivatives a long time ago and dismissed them as not practical. If you want to dig into this study the Gamma function. Combine this with adaptive shock absorbers which can act like an overdamped function and suspension science is starting to act more like a science. If you are interested in overdamped suspensions you need to study complex numbers. I've talked about active shocks here and suggested they can function as regenerative chargers.