Simplify Challenging Software Problems with Rocket Science

Aerospace engineering is really no more magical than programming, and yet it's shrouded in such mystery and mysticism that practically no one bothers to study it. I'll show you how to apply concepts from rocket science to challenging software problems, allowing you to spend more time coming up with answers rather than interpreting inputs. We'll also learn to control the universe outside our glowing rectangles.

Transcript

1. Simplify Challenging Software Problems with Rocket Science @bendyworks Brad Grzesiak — @listrophy
2. –Ashe Dryden “Whenever Brad is drinking, you wanna make sure you're sitting next to him, because instead of being obnoxious, he teaches you orbital mechanics.”
3. Heads up: 1 Animated GIF
4. Agenda • Reduce Cognitive Load • Visualize Simulations with Graphics • Control and Respond to Real World Processes
5. Agenda • Reduce Cognitive Load • Visualize Simulations with Graphics • Control and Respond to Real World Processes
6. we are not superheros
7. Scalars & Collections Primitives & Arrays • x, y, z = 2, 3, 5 • Math.sqrt(x**2 + y**2 + z**2) • array.zip(other).map{|(i,j)| i+j} • [m[0][0]*v[0]+m[0][1]*v[1], m[1][0]*v[0]+m[1][1]*v[1]] Vectors & Matrices • vector = Vector[2, 3, 5] • vector.magnitude # or vector.r • vector_1 + vector_2 • matrix * vector

8. “matrix” “times” “vector?”
9. Linear Transformations • Scale, Rotate, Skew, Translate (with a trick) • Common in CSS3 • Common in Kinetics & Kinematics
10. Matrix Times Vector 1.  ⽷a    b⽹⽷x⽹        ⽸c    d⽺⽸y⽺   2.  ［x    y］        ⽷a    b⽹        ⽸c    d⽺   3.  ⽷ax+by⽹        ⽸cx+dy⽺  
11. Matrix Times Vector def matrix_times_vector(m, v) a, b = m[0] c, d = m[1] x, y = v [ a*x + b*y, c*x + d*y ] end require 'matrix' def matrix_times_vector(m, v) m * v end NOW WITH DIM CHECKS!
12. Rotation Matrix R(θ)  =  ⽷cosθ  -­‐sinθ⽹                ⽸sinθ    cosθ⽺   R(30deg)*⟨1,0⟩  =  ⟨0.87,0.5⟩   R(90deg)*⟨1,0⟩  =  ⟨0,1⟩
13. Rotation Matrix R(-­‐30deg)*                        =  
14. Agenda • Reduce Cognitive Load • Visualize Simulations with Graphics • Control and Respond to Real World Processes
15. Why Graphic Simulations? • Complex Systems • High Sensitivity • Pattern Recognition Required • Seeking “Good Enough”
16. In Aerospace Engineering • Launch Vibration Testing • “Kick” tests • Thermal Equilibrium • Designing to Safety Factor
17. In Aerospace Engineering • Launch Vibration Testing • “Kick” tests • Thermal Equilibrium • Designing to Safety Factor • N-Body Orbital Trajectories
18. The n-Body Problem • Newton’s Laws + Gravity • Solved for N=2 • For N>2, “no general analytical solution,” except for special cases (e.g., Lagrangian Points)
19. The n-Body Problem Gravity Force = x Newton’s 2nd Law Force = mass ⨉ acceleration Newton’s 3rd Law Force₁ = -Force₂ Velocity-Acceleration Position-Velocity
20. Wait a minute. Derivatives?
21. Formal Derivative
22. Our Approximation
23. Our Approximation
24. Our Approximation
25. The n-Body Problem Gravity Force = x Newton’s 2nd Law Force = mass ⨉ acceleration Newton’s 3rd Law Force₁ = -Force₂ Velocity-Acceleration Position-Velocity
26. The n-Body Problem Gravity Force = x Newton’s 2nd Law Force = mass ⨉ acceleration Newton’s 3rd Law Force₁ = -Force₂ Velocity-Acceleration vnow = vprev + anow dt Position-Velocity xnow = xprev + vnow dt
27. The n-Body Problem Gravity Force = x Newton’s 2nd Law acceleration = Force ÷ mass Newton’s 3rd Law Force₁ = -Force₂ Velocity-Acceleration vnow = vprev + anow dt Position-Velocity xnow = xprev + vnow dt
28. Gravity Fnow = x Newton’s 2nd Law anow = Fnow ÷ m Newton’s 3rd Law (loop over each mass-pair) Velocity-Acceleration vnow = vprev + anow dt Position-Velocity xnow = xprev + vnow dt The n-Body Problem
29. The n-Body Problem bodies.map do |body| [body, gravity(body, bodies-[body])] end.each do |(body, force)| accel = force / body.mass body.velocity += accel * dt body.position += body.velocity * dt end
30. The n-Body Problem def gravity(body, others) others.reduce(Vector[0,0]) do |memo, other| offset = other.position - body.position memo + offset * G * body.mass * other.mass / offset.r**3 end end
31. (demo)
32. Agenda • Reduce Cognitive Load • Visualize Simulations with Graphics • Control and Respond to Real World Processes
33. The World is Complicated • “Assume no air resistance” • “Assume a frictionless surface” • “Assume perfect DC voltage” • “Assume no impact from general or special relativity”
34. You simply cannot predefine a specific solution to a problem that is perturbed by the real world
35. –Helmuth von Moltke the Elder “No battle plan ever survives contact with the enemy.”
36. The Answer: React
37. Feedback Controller
38. Feedback Controller
39. Feedback Controller
40. PID Controller
41. Controller P I D roportional ntegral erivative
42. Feedback Controller diff == error
43. Proportional P  =  error  =  desired  -­‐  actual
44. Derivative D  =  (error  -­‐  prev_error)/dt
45. Integral I  =  I  +  error*dt
46. Our PID Controller loop do sleep 0.2 curr_time = Time.now dt = curr_time - prev_time p = error = desired - actual i = i + error * dt d = (error - prev_error)/dt setThrust(0.1*p + 0.003*i + 0.08*d) prev_error, prev_time = error, curr_time end
47. (demo)
48. Agenda • Reduce Cognitive Load • Visualize Simulations with Graphics • Control and Respond to Real World Processes
49. Photo Credits • “ABS/EUTELSAT-1 Launch” (Public Domain):
 http://www.spacex.com/media-gallery/detail/127081/4896 • “Beer Actor” (CC-BY):
 https://www.flickr.com/photos/cogdog/21127813750/ • “Up, up and away!” (CC-BY-SA):
 https://www.flickr.com/photos/kindercapes/5694816038 • “I’m confused” (CC-BY-SA):
 https://www.flickr.com/photos/doctabu/342220423 • “Cookie Monster Waiting” (no idea):
 https://www.google.com/search?q=cookie+monster+waiting • “Elmer Pump Heat Equation” (CC-BY-SA):
 https://commons.wikimedia.org/wiki/File:Elmer-pump-heatequation.png • “Owl Stuck” (CC-BY):
 https://www.flickr.com/photos/eben-frostey/7147015007

50. Thank You! Brad Grzesiak brad@bendyworks.com @listrophy