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Tony Wilson
The Math Sorcerer
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Comments by "Tony Wilson" (@tonywilson4713) on "The Only Engineering Video You Will Ever Need" video.
AEROSPACE ENGINEER HERE: I was well prepared to dismiss vid this straight out of hand as yet another crap explanation of engineering, but I am quite happy to say he's hit the spot. What so many people miss is that engineering is fundamentally the art of APPLIED MATH as opposed to pure math or theoretical math. Fundamentally engineers take math and APPLY it to real world problems, but to get to that point we have to learn a staggering amount of math to have the skills needed. Aerospace is particularly brutal in this respect. I had to do 2 extra pure math classes than other engineers. One was in vectors & matrices which was fairly straight forward and I'd expect most engineers to pass it. The other was in advanced calculus which we needed for things like aerodynamics. It was brutally hard and we had a professor who was a real life Sheldon Cooper except he was even more arrogant. By far the single hardest class I took was Spacecraft Dynamics. We had to do 2 high level aerospace classes to graduate. All of us took Finite Element Methods because that's reasonably straight forward applied matrix methods. After FEM most people took orbital mechanics because that was a favorite of the satellite industry. OM isn't easy and involves a lot of differential calculus in 3-d and in spherical coordinate systems. 4 or 5 of us (wanting to be different) took Spacecraft Dynamics and regretted it about 5 minutes into the first lecture. There were about 8 or 9 post grads doing the higher level variant of the class which meant they had to do a term paper and by term paper I mean a journal type technical paper. The difference between orbital mechanics and space craft dynamics is that OM is about calculating orbits, transfers and trajectories while spacecraft dynamics is how you get a spacecraft to point where you want as is flies along its orbit/trajectory. The problem with spacecraft dynamics is that it involves free body mechanics where every action has its opposite response. Satellites are NOT attached to something large and solid like a planet. So if you do something like turn the antenna on a satellite then the rest of the satellite wants to go the in the opposite direction. Since a lot of satellite stability involves gyroscopes or reaction wheels then that math gets convoluted very quickly because of precession. What makes it truly ugly is that a satellite typically has 6 degrees of freedom - X, Y, Z and roll, pitch and yaw, which as the X, Y, X suggests is done in cartesian coordinates.*BUT* if the roll pitch and yaw is done with gyroscopes or reaction wheels then that part of the system is in cylindrical coordinates and need translating into cartesian. The problem is that satellites move in spherical coordinate systems. So you have a convoluted set of differential equations 1/2 in cartesian and 1/2 in cylindrical that need translating into a spherical coordinate system AND THEN you have to solve that system for what you actually want to do. And for those who are wondering this is what makes keeping the ISS in the right orientation so damn hard and what made the US Star Wars program so close to impossible they gave up. And so you all know I did that class in1987 and ALL of the postgrads were on DARPA funded scholarships doing Star Wars stuff.
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