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Cell[BoxData[
    \(\(\( (*\ rigid\ body\ dynamics\ *) \)\(\[IndentingNewLine]\)\( (*\ 
      uses\ omega\ cross\ rotation\ matrix\ columns\ for\ orientation - 
        dot\ *) \)\(\[IndentingNewLine]\)\( (*\ 
      this\ normalizes\ the\ orient\ matrix\ after\ update\ *) \)\(\
\[IndentingNewLine]\)\(<< Calculus`VectorAnalysis`\)\)\)], "Input"],

Cell[BoxData[
    \(\(\( (*\ object\ data\ structure\ *) \)\(\[IndentingNewLine]\)\( (*\ 
      constants : \ mass, \ inertia\ tensor, \ 
      inverse\ of\ inertia\ tensor; \ state\ \(variables : \ position\), \ 
      orientation, \ momentum, \ angular\ momentum; \ 
      auxiliary\ \(variables : \ velocity\), \ 
      angular\ velocity, \ \[IndentingNewLine]velocity, \ rotation - dot, \ 
      force, \ torque\ *) \)\(\[IndentingNewLine]\)\(object\  = {\
\[IndentingNewLine] (*\ 
            geometry\ definition\ *) \[IndentingNewLine]{{\(-4\), 
              4}, {\(-2\), 2}, {\(-1\), 1}}, \ \ \ \ \ \ \ \ \ \ \ \ \  (*\ 
            min/max\ in\ x, y, z*) \[IndentingNewLine] (*\ 
            constants\ *) \[IndentingNewLine]20, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  (*\ 
            mass\ *) \[IndentingNewLine]{{40, 0, 0}, {0, 20, 0}, {0, 0, 
              10}}, \  (*\ 
            I\ *) \[IndentingNewLine]{{1, 0, 0}, {0, 1, 0}, {0, 0, 
              1}}, \  (*\ I\ inverse\ *) \[IndentingNewLine] (*\ 
            state\ variables\ *) \[IndentingNewLine]{0, 0, 
            0}, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  (*\ 
            position\ *) \[IndentingNewLine]{{1, 0, 0}, {0, 1, 0}, {0, 0, 
              1}},  (*\ orientation\ *) \[IndentingNewLine]{0, 0, 
            0}, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  (*\ 
            momentum\ *) \[IndentingNewLine]{0, 0, 
            0}, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  (*\ 
            angular\ momentum\ *) \[IndentingNewLine] (*\ 
            auxiliary\ variables\ *) \[IndentingNewLine]{0, 0, 
            0}, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  (*\ 
            velocity\ *) \[IndentingNewLine]{{1, 0, 0}, {0, 1, 0}, {0, 0, 
              1}}, \  (*\ I\ inverse\ \((time)\)\ *) \[IndentingNewLine]{0, 
            0, 
            0}, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  (*\ 
            angular\ velocity\ *) \[IndentingNewLine] (*\ 
            derivative\ variables\ *) \[IndentingNewLine]{0, 0, 
            0}, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  (*\ 
            velocity\ *) \[IndentingNewLine]{{1, 0, 0}, {0, 1, 0}, {0, 0, 
              1}}, \  (*\ orientation\ dot\ *) \[IndentingNewLine]{0, 0, 
            0}, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  (*\ 
            force\ *) \[IndentingNewLine]{0, 0, 
            0}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  (*\ 
            torque\ *) \[IndentingNewLine]};\)\)\)], "Input"],

Cell[BoxData[
    \(\(object\  = 
        ReplacePart[object, Inverse[object[\([3]\)]], 4];\)\)], "Input"],

Cell[BoxData[{
    \( (*\ define\ access\ functions\ *) \[IndentingNewLine]mass[obj_]\  := \ 
      obj[\([2]\)]\), "\[IndentingNewLine]", 
    \(inertia[obj_] := obj[\([3]\)]\), "\[IndentingNewLine]", 
    \(inertiaInv[obj_] := obj[\([4]\)]\), "\[IndentingNewLine]", 
    \(position[obj_]\  := \ obj[\([5]\)]\), "\[IndentingNewLine]", 
    \(orient[obj_]\  := \ obj[\([6]\)]\), "\[IndentingNewLine]", 
    \(momentum[obj_]\  := \ obj[\([7]\)]\), "\[IndentingNewLine]", 
    \(angularMomentum[obj_]\  := \ obj[\([8]\)]\), "\[IndentingNewLine]", 
    \(velocityAux[obj_]\  := \ obj[\([9]\)]\), "\[IndentingNewLine]", 
    \(Iinv[obj_]\  := \ obj[\([10]\)]\), "\[IndentingNewLine]", 
    \(omega[obj_] := obj[\([11]\)]\), "\[IndentingNewLine]", 
    \(velocity[obj_]\  := \ obj[\([12]\)]\), "\[IndentingNewLine]", 
    \(orientDot[obj_] := obj[\([13]\)]\), "\[IndentingNewLine]", 
    \(force[obj_] := obj[\([14]\)]\), "\[IndentingNewLine]", 
    \(torque[obj_] := obj[\([15]\)]\), "\[IndentingNewLine]", 
    \(setPosition[obj_, value_] := 
      ReplacePart[obj, value, 5]\), "\[IndentingNewLine]", 
    \(setOrient[obj_, value_]\  := \ 
      ReplacePart[obj, value, 6]\), "\[IndentingNewLine]", 
    \(setMomentum[obj_, value_]\  := \ 
      ReplacePart[obj, value, 7]\), "\[IndentingNewLine]", 
    \(setAngularMomentum[obj_, value_] := 
      ReplacePart[obj, value, 8]\), "\[IndentingNewLine]", 
    \(setVelocityAux[obj_, value_] := 
      ReplacePart[obj, value, 9]\), "\[IndentingNewLine]", 
    \(setIinverse[obj_, value_]\  := 
      ReplacePart[obj, value, 10]\), "\[IndentingNewLine]", 
    \(setOmega[obj_, value_]\  := 
      ReplacePart[obj, value, 11]\), "\[IndentingNewLine]", 
    \(setVelocity[obj_, value_] := 
      ReplacePart[obj, value, 12]\), "\[IndentingNewLine]", 
    \(setOrientDot[obj_, value_] := 
      ReplacePart[obj, value, 13]\), "\[IndentingNewLine]", 
    \(\(setForce[obj_, value_]\  := \ 
        ReplacePart[obj, value, 14];\)\), "\[IndentingNewLine]", 
    \(setTorque[obj_, value_]\  := 
      ReplacePart[obj, value, 15]\), "\[IndentingNewLine]", 
    \(addForce[obj_, value_] := \ 
      setForce[obj, force[obj] + value]\), "\[IndentingNewLine]", 
    \(addTorque[obj_, value_] := 
      setTorque[obj, torque[obj] + value]\[IndentingNewLine]\ \)}], "Input"],

Cell[BoxData[
    \(\(\( (*\ 
      compute\ auxiliary\ variables\ *) \)\(\[IndentingNewLine]\)\(computeAux[
        obj_]\  := \ \((\[IndentingNewLine]a1 = 
          setVelocityAux[obj, 
            momentum[obj]/mass[obj]]; \[IndentingNewLine]a2 = 
          setIinverse[a1, 
            orient[a1] . inertiaInv[a1] . 
              Inverse[orient[a1]]]; \[IndentingNewLine]setOmega[a2, 
          inertiaInv[a2] . 
            angularMomentum[a2]]\[IndentingNewLine])\)\)\)\)], "Input"],

Cell[BoxData[
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      compute\ additional\ derivative\ information\ *) \
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          setVelocity[obj, velocityAux[obj]]; \[IndentingNewLine]dw = 
          omega[d1]; \[IndentingNewLine]d2 = 
          Transpose[orient[d1]]; \[IndentingNewLine]setOrientDot[d1, 
          Transpose[{CrossProduct[dw, d2[\([1]\)]], 
              CrossProduct[dw, d2[\([2]\)]], 
              CrossProduct[dw, 
                d2[\([3]\)]]}]]\[IndentingNewLine])\)\(\[IndentingNewLine]\)\)\
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Cell[BoxData[
    \(\(\( (*\ 
      update\ orientation\ matrix\ and\ renormalize\ the\ rows\ *) \)\(\
\[IndentingNewLine]\)\(updateObject[obj_, 
        dt_] := \((\[IndentingNewLine]u1 = \ 
          setPosition[obj, 
            position[obj] + velocity[obj]*dt]; \[IndentingNewLine]u2 = 
          setOrient[u1, 
            orient[u1] + orientDot[u1]*dt]; \[IndentingNewLine]u3 = 
          setMomentum[u2, 
            momentum[u2] + force[u2]*dt]; \[IndentingNewLine]u4\  = \ 
          setAngularMomentum[u3, 
            angularMomentum[u3] + torque[u3]*dt]; \[IndentingNewLine]u5\  = \ 
          setForce[u4, {0, 0, 0}]; \[IndentingNewLine]u6\  = \ 
          setTorque[u5, {0, 0, 0}]; \[IndentingNewLine] (*\ 
          normalize\ orient\ matrix\ *) \[IndentingNewLine]u7 = 
          orient[u6]; \[IndentingNewLine]u8 = 
          u7[\([1]\)]; \[IndentingNewLine]len = 
          Sqrt[u8[\([1]\)]*u8[\([1]\)] + u8[\([2]\)]*u8[\([2]\)] + 
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          Sqrt[u8[\([1]\)]*u8[\([1]\)] + u8[\([2]\)]*u8[\([2]\)] + 
              u8[\([3]\)]*u8[\([3]\)]]; \[IndentingNewLine]u92 = 
          u8/len; \[IndentingNewLine]u8 = 
          u7[\([3]\)]; \[IndentingNewLine]len = 
          Sqrt[u8[\([1]\)]*u8[\([1]\)] + u8[\([2]\)]*u8[\([2]\)] + 
              u8[\([3]\)]*u8[\([3]\)]]; \[IndentingNewLine]u93 = 
          u8/len; \[IndentingNewLine]u10 = 
          setOrient[u6, {u91, u92, u93}]\[IndentingNewLine])\)\)\)\)], "Input"],

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          m . {x0, y0, z1} + pos; \[IndentingNewLine]p010 = 
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