The periodic motion of a bird's wings could be modelled in the complex domain as some kind of deformed circle. But I barely remember the mathematics behind oscillating systems beyond the Laplace Transform.
Discussion
Had to google that 🥲 I don't know that I ever really learned much about them, but very vaguely rings a bell when I read about it
I remember spending months doing Laplace transforms in college until I could do them in my sleep. The more practical engineering equations are big on that stuff. Alternating current systems especially, but also rotating machinery.
So sad that I can't even remember what they are. Is that the integration with 1/S?
I googled and remembered that it's a section of the Euler curve, which is a curve who's curvature increases linearly along its length.
So the clothoid loop is the portion of the Euler curve that moves from the origin to its highest point, then mirrored so that it comes back down. It's like taking a turn in your car and turning the steering wheel at a constant rate.
I can't remember the exact way to form the integral or what it's used for. But I do know that you can't solve the integral analytically.
Think he meant the even more basic idea of laplace transforms. Clothoid loop shmothoid poop. Fake math
That's as far as my brain will take me without opening a textbook 😅😂
