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
   

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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.”
   

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3. Heads up:
   1 Animated GIF
   

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4. Agenda
   • Reduce Cognitive Load
   • Visualize Simulations with Graphics
   • Control and Respond to Real World Processes
   

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5. Agenda
   • Reduce Cognitive Load
   • Visualize Simulations with Graphics
   • Control and Respond to Real World Processes
   

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6. we
   are
   not
   superheros
   

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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

   

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8. “matrix”
   “times”
   “vector?”
   

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9. Linear Transformations
   • Scale, Rotate, Skew, Translate (with a trick)
   • Common in CSS3
   • Common in Kinetics & Kinematics
   

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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  
    

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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!
    

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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⟩
    

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13. Rotation Matrix
    R(-­‐30deg)*                        =  
    

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14. Agenda
    • Reduce Cognitive Load
    • Visualize Simulations with Graphics
    • Control and Respond to Real World Processes
    

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15. Why Graphic Simulations?
    • Complex Systems
    • High Sensitivity
    • Pattern Recognition Required
    • Seeking “Good Enough”
    

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16. In Aerospace Engineering
    • Launch Vibration Testing
    • “Kick” tests
    • Thermal Equilibrium
    • Designing to Safety Factor
    

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17. In Aerospace Engineering
    • Launch Vibration Testing
    • “Kick” tests
    • Thermal Equilibrium
    • Designing to Safety Factor
    • N-Body Orbital Trajectories
    

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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)
    

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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
    

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20. Wait a minute.
    Derivatives?
    

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21. Formal Derivative
    

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22. Our Approximation
    

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23. Our Approximation
    

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24. Our Approximation
    

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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
    

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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
    

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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
    

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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
    

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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
    

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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
    

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31. (demo)
    

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32. Agenda
    • Reduce Cognitive Load
    • Visualize Simulations with Graphics
    • Control and Respond to Real World Processes
    

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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”
    

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34. You simply cannot predefine a
    specific solution to a problem that
    is perturbed by the real world
    

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35. –Helmuth von Moltke the Elder
    “No battle plan ever survives
    contact with the enemy.”
    

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36. The Answer: React
    

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37. Feedback Controller
    

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38. Feedback Controller
    

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39. Feedback Controller
    

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40. PID Controller
    

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41. Controller
    P
    I
    D
    roportional
    ntegral
    erivative
    

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42. Feedback Controller
    diff == error
    

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43. Proportional
    P  =  error  =  desired  -­‐  actual
    

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44. Derivative
    D  =  (error  -­‐  prev_error)/dt
    

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45. Integral
    I  =  I  +  error*dt
    

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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
    

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47. (demo)
    

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48. Agenda
    • Reduce Cognitive Load
    • Visualize Simulations with Graphics
    • Control and Respond to Real World Processes
    

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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

    

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

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