Date: 10 May 2013

theta1516actual = 4.869468613064179
theta1415actual = 4.806636759992384
theta12actual = 0.3141592653589793
X0actual = (0.3, 0)
theta01actual = 0.39269908169872414
snapthreshold = 0.01
theta23actual = 0.47123889803846897
theta34actual = 1.2566370614359172
theta56actual = 1.7278759594743864
theta67actual = 1.8849555921538759
theta78actual = 2.356194490192345
theta89actual = 2.827433388230814
theta910actual = 2.9845130209103035
theta1112actual = 3.707079331235956
theta1213actual = 4.115486376202629
dvsol = 0.2
dwsol = 0.02
theta1314actual = 4.71238898038469
theta1011actual = 3.141592653589793
theta45actual = 1.5707963267948966
a = 0.2
vnullrightmaxv: (1 + a + sqrt(1 - a + a^(2))) / 3
epsilon = 0.01
gamm = 2
vmax = 1.1
vmin = -0.27
wmin = -0.03
wmax = 0.13
dvdt(v, w) = (((-v) * (v - a)) * (v - 1)) - w
dwdt(v, w) = (epsilon * (v - (gamm * w)))
vecfieldmag(v, w) = sqrt((dvdt(v, w) / vmax)^(2) + (dwdt(v, w) / wmax)^(2))
dvdtnorm(v, w) = dvdt(v, w) / vecfieldmag(v, w)
dwdtnorm(v, w) = dwdt(v, w) / vecfieldmag(v, w)
v01 = 0.430629213483146
v02 = 0.5638426966292135
ngrid = 10
vecmult = 0.9
x01actual = Vector(((cos(theta01actual) * dvsol), (sin(theta01actual) * dwsol)))
X1actual: X0actual + x01actual
x12actual = Vector(((cos(theta12actual) * dvsol), (sin(theta12actual) * dwsol)))
X2actual: X1actual + x12actual
x23actual = Vector(((cos(theta23actual) * dvsol), (sin(theta23actual) * dwsol)))
X3actual: X2actual + x23actual
x34actual = Vector(((cos(theta34actual) * dvsol), (sin(theta34actual) * dwsol)))
X4actual: X3actual + x34actual
x45actual = Vector(((cos(theta45actual) * dvsol), (sin(theta45actual) * dwsol)))
X5actual: X4actual + x45actual
x56actual = Vector(((cos(theta56actual) * dvsol), (sin(theta56actual) * dwsol)))
X6actual: X5actual + x56actual
x67actual = Vector(((cos(theta67actual) * dvsol), (sin(theta67actual) * dwsol)))
X7actual: X6actual + x67actual
x78actual = Vector(((cos(theta78actual) * dvsol), (sin(theta78actual) * dwsol)))
X8actual: X7actual + x78actual
x89actual = Vector(((cos(theta89actual) * dvsol), (sin(theta89actual) * dwsol)))
X9actual: X8actual + x89actual
x910actual = Vector(((cos(theta910actual) * dvsol), (sin(theta910actual) * dwsol)))
X10actual: X9actual + x910actual
x1011actual = Vector(((cos(theta1011actual) * dvsol), (sin(theta1011actual) * dwsol)))
X11actual: X10actual + x1011actual
x1112actual = Vector(((cos(theta1112actual) * dvsol), (sin(theta1112actual) * dwsol)))
X12actual: X11actual + x1112actual
x1213actual = Vector(((cos(theta1213actual) * dvsol), (sin(theta1213actual) * dwsol)))
X13actual: X12actual + x1213actual
x1314actual = Vector(((cos(theta1314actual) * dvsol), (sin(theta1314actual) * dwsol)))
X14actual: X13actual + x1314actual
x1415actual = Vector(((cos(theta1415actual) * dvsol), (sin(theta1415actual) * dwsol)))
X15actual: X14actual + x1415actual
x1516actual = Vector(((cos(theta1516actual) * dvsol), (sin(theta1516actual) * dwsol)))
X16actual: X15actual + x1516actual
theta1718actual = 5.237034953534185
x1718actual = Vector((((cos(theta1718actual) * dvsol) * 1.01), ((sin(theta1718actual) * dwsol) * 1.01)))
Y0actual = (0.17, 0)
dvsol2 = 0.08
dwsol2 = 0.016
phi01actual = 1.8849555921538759
y01actual = Vector(((cos(phi01actual) * dvsol2), (sin(phi01actual) * dwsol2)))
Y1actual: Y0actual + y01actual
phi12actual = 2.199114857512855
y12actual = Vector(((cos(phi12actual) * dvsol2), (sin(phi12actual) * dwsol2)))
Y2actual: Y1actual + y12actual
phi23actual = 3.141592653589793
y23actual = Vector(((cos(phi23actual) * dvsol2), (sin(phi23actual) * dwsol2)))
Y3actual: Y2actual + y23actual
phi34actual = 3.455751918948773
y34actual = Vector(((cos(phi34actual) * dvsol2), (sin(phi34actual) * dwsol2)))
Y4actual: Y3actual + y34actual
phi45actual = 4.71238898038469
y45actual = Vector((((cos(phi45actual) * dvsol2) * 0.78), ((sin(phi45actual) * dwsol2) * 0.78)))
Y5actual: Y4actual + y45actual
phi56actual = 5.529203070318036
y56actual = Vector(((cos(phi56actual) * dvsol2), (sin(phi56actual) * dwsol2)))
Y6actual: Y5actual + y56actual
dt = 0.5
tmin = -0.8
tmax = 10.5
Y7actual = (0, 0)
Y8actual = (0, 0)
Y9actual = (0, 0)
Y10actual = (0, 0)
dv = 0.25
v0actual: x(X0actual)
v1actual: x(X1actual)
v2actual: x(X2actual)
v3actual: x(X3actual)
v4actual: x(X4actual)
v5actual: x(X5actual)
v6actual: x(X6actual)
v7actual: x(X7actual)
v8actual: x(X8actual)
v9actual: x(X9actual)
v10actual: x(X10actual)
v0possibilities = Sequence(((0 * dt), v0actual + i), i, (ceil((vmin - v0actual) / dv) * dv), vmax - v0actual, dv)
v1possibilities = Sequence((dt, v1actual + i), i, (ceil((vmin - v1actual) / dv) * dv), vmax - v1actual, dv)
v2possibilities = Sequence(((2 * dt), v2actual + i), i, (ceil((vmin - v2actual) / dv) * dv), vmax - v2actual, dv)
v3possibilities = Sequence(((3 * dt), v3actual + i), i, (ceil((vmin - v3actual) / dv) * dv), vmax - v3actual, dv)
v4possibilities = Sequence(((4 * dt), v4actual + i), i, (ceil((vmin - v4actual) / dv) * dv), vmax - v4actual, dv)
v5possibilities = Sequence(((5 * dt), v5actual + i), i, (ceil((vmin - v5actual) / dv) * dv), vmax - v5actual, dv)
v6possibilities = Sequence(((6 * dt), v6actual + i), i, (ceil((vmin - v6actual) / dv) * dv), vmax - v6actual, dv)
v7possibilities = Sequence(((7 * dt), v7actual + i), i, (ceil((vmin - v7actual) / dv) * dv), vmax - v7actual, dv)
v8possibilities = Sequence(((8 * dt), v8actual + i), i, (ceil((vmin - v8actual) / dv) * dv), vmax - v8actual, dv)
v9possibilities = Sequence(((9 * dt), v9actual + i), i, (ceil((vmin - v9actual) / dv) * dv), vmax - v9actual, dv)
v10possibilities = Sequence(((10 * dt), v10actual + i), i, (ceil((vmin - v10actual) / dv) * dv), vmax - v10actual, dv)
V0 = Point(v0possibilities)
V1 = Point(v1possibilities)
V2 = Point(v2possibilities)
V3 = Point(v3possibilities)
V4 = Point(v4possibilities)
V5 = Point(v5possibilities)
V6 = Point(v6possibilities)
V7 = Point(v7possibilities)
V8 = Point(v8possibilities)
V9 = Point(v9possibilities)
V10 = Point(v10possibilities)
dw = 0.025
w0actual: y(X0actual)
w1actual: y(X1actual)
w2actual: y(X2actual)
w3actual: y(X3actual)
w4actual: y(X4actual)
w5actual: y(X5actual)
w6actual: y(X6actual)
w7actual: y(X7actual)
w8actual: y(X8actual)
w9actual: y(X9actual)
w10actual: y(X10actual)
w0possibilities = Sequence(((0 * dt), w0actual + i), i, (ceil((wmin - w0actual) / dw) * dw), wmax - w0actual, dw)
w1possibilities = Sequence((dt, w1actual + i), i, (ceil((wmin - w1actual) / dw) * dw), wmax - w1actual, dw)
w2possibilities = Sequence(((2 * dt), w2actual + i), i, (ceil((wmin - w2actual) / dw) * dw), wmax - w2actual, dw)
w3possibilities = Sequence(((3 * dt), w3actual + i), i, (ceil((wmin - w3actual) / dw) * dw), wmax - w3actual, dw)
w4possibilities = Sequence(((4 * dt), w4actual + i), i, (ceil((wmin - w4actual) / dw) * dw), wmax - w4actual, dw)
w5possibilities = Sequence(((5 * dt), w5actual + i), i, (ceil((wmin - w5actual) / dw) * dw), wmax - w5actual, dw)
w6possibilities = Sequence(((6 * dt), w6actual + i), i, (ceil((wmin - w6actual) / dw) * dw), wmax - w6actual, dw)
w7possibilities = Sequence(((7 * dt), w7actual + i), i, (ceil((wmin - w7actual) / dw) * dw), wmax - w7actual, dw)
w8possibilities = Sequence(((8 * dt), w8actual + i), i, (ceil((wmin - w8actual) / dw) * dw), wmax - w8actual, dw)
w9possibilities = Sequence(((9 * dt), w9actual + i), i, (ceil((wmin - w9actual) / dw) * dw), wmax - w9actual, dw)
w10possibilities = Sequence(((10 * dt), w10actual + i), i, (ceil((wmin - w10actual) / dw) * dw), wmax - w10actual, dw)
W0 = Point(w0possibilities)
W1 = Point(w1possibilities)
W2 = Point(w2possibilities)
W3 = Point(w3possibilities)
W4 = Point(w4possibilities)
W5 = Point(w5possibilities)
W6 = Point(w6possibilities)
W7 = Point(w7possibilities)
W8 = Point(w8possibilities)
W9 = Point(w9possibilities)
W10 = Point(w10possibilities)
v0correct: y(V0) ≟ v0actual
v1correct: y(V1) ≟ v1actual
v2correct: y(V2) ≟ v2actual
v3correct: y(V3) ≟ v3actual
v4correct: y(V4) ≟ v4actual
v5correct: y(V5) ≟ v5actual
v6correct: y(V6) ≟ v6actual
v7correct: y(V7) ≟ v7actual
v8correct: y(V8) ≟ v8actual
v9correct: y(V9) ≟ v9actual
v10correct: y(V10) ≟ v10actual
w0correct: y(W0) ≟ w0actual
w1correct: y(W1) ≟ w1actual
w2correct: y(W2) ≟ w2actual
w3correct: y(W3) ≟ w3actual
w4correct: y(W4) ≟ w4actual
w5correct: y(W5) ≟ w5actual
w6correct: y(W6) ≟ w6actual
w7correct: y(W7) ≟ w7actual
w8correct: y(W8) ≟ w8actual
w9correct: y(W9) ≟ w9actual
w10correct: y(W10) ≟ w10actual
X19actual = (0, 0)
X20actual = (0, 0)
v11actual: x(X11actual)
v12actual: x(X12actual)
v13actual: x(X13actual)
v14actual: x(X14actual)
v15actual: x(X15actual)
v16actual: x(X16actual)
v19actual: x(X19actual)
v20actual: x(X20actual)
v11possibilities = Sequence(((11 * dt), v11actual + i), i, (ceil((vmin - v11actual) / dv) * dv), vmax - v11actual, dv)
v12possibilities = Sequence(((12 * dt), v12actual + i), i, (ceil((vmin - v12actual) / dv) * dv), vmax - v12actual, dv)
v13possibilities = Sequence(((13 * dt), v13actual + i), i, (ceil((vmin - v13actual) / dv) * dv), vmax - v13actual, dv)
v14possibilities = Sequence(((14 * dt), v14actual + i), i, (ceil((vmin - v14actual) / dv) * dv), vmax - v14actual, dv)
v15possibilities = Sequence(((15 * dt), v15actual + i), i, (ceil((vmin - v15actual) / dv) * dv), vmax - v15actual, dv)
v16possibilities = Sequence(((16 * dt), v16actual + i), i, (ceil((vmin - v16actual) / dv) * dv), vmax - v16actual, dv)
v19possibilities = Sequence(((19 * dt), v19actual + i), i, (ceil((vmin - v19actual) / dv) * dv), vmax - v19actual, dv)
v20possibilities = Sequence(((20 * dt), v20actual + i), i, (ceil((vmin - v20actual) / dv) * dv), vmax - v20actual, dv)
theta1617actual = 4.90088
x1617actual = Vector(((cos(theta1617actual) * dvsol), (sin(theta1617actual) * dwsol)))
X17actual: X16actual + x1617actual
X18actual: X17actual + x1718actual
v17actual: x(X17actual)
v18actual: x(X18actual)
v17possibilities = Sequence(((17 * dt), v17actual + i), i, (ceil((vmin - v17actual) / dv) * dv), vmax - v17actual, dv)
v18possibilities = Sequence(((18 * dt), v18actual + i), i, (ceil((vmin - v18actual) / dv) * dv), vmax - v18actual, dv)
V11 = Point(v11possibilities)
V12 = Point(v12possibilities)
V13 = Point(v13possibilities)
V14 = Point(v14possibilities)
V15 = Point(v15possibilities)
V16 = Point(v16possibilities)
V17 = Point(v17possibilities)
V18 = Point(v18possibilities)
V19 = Point(v19possibilities)
V20 = Point(v20possibilities)
w11actual: y(X11actual)
w12actual: y(X12actual)
w13actual: y(X13actual)
w14actual: y(X14actual)
w15actual: y(X15actual)
w16actual: y(X16actual)
w17actual: y(X17actual)
w18actual: y(X18actual)
w19actual: y(X19actual)
w20actual: y(X20actual)
w11possibilities = Sequence(((11 * dt), w11actual + i), i, (ceil((wmin - w11actual) / dw) * dw), wmax - w11actual, dw)
w12possibilities = Sequence(((12 * dt), w12actual + i), i, (ceil((wmin - w12actual) / dw) * dw), wmax - w12actual, dw)
w13possibilities = Sequence(((13 * dt), w13actual + i), i, (ceil((wmin - w13actual) / dw) * dw), wmax - w13actual, dw)
w14possibilities = Sequence(((14 * dt), w14actual + i), i, (ceil((wmin - w14actual) / dw) * dw), wmax - w14actual, dw)
w15possibilities = Sequence(((15 * dt), w15actual + i), i, (ceil((wmin - w15actual) / dw) * dw), wmax - w15actual, dw)
w16possibilities = Sequence(((16 * dt), w16actual + i), i, (ceil((wmin - w16actual) / dw) * dw), wmax - w16actual, dw)
w17possibilities = Sequence(((17 * dt), w17actual + i), i, (ceil((wmin - w17actual) / dw) * dw), wmax - w17actual, dw)
w18possibilities = Sequence(((18 * dt), w18actual + i), i, (ceil((wmin - w18actual) / dw) * dw), wmax - w18actual, dw)
w19possibilities = Sequence(((19 * dt), w19actual + i), i, (ceil((wmin - w19actual) / dw) * dw), wmax - w19actual, dw)
w20possibilities = Sequence(((20 * dt), w20actual + i), i, (ceil((wmin - w20actual) / dw) * dw), wmax - w20actual, dw)
W11 = Point(w11possibilities)
W12 = Point(w12possibilities)
W13 = Point(w13possibilities)
W14 = Point(w14possibilities)
W15 = Point(w15possibilities)
W16 = Point(w16possibilities)
W17 = Point(w17possibilities)
W18 = Point(w18possibilities)
W19 = Point(w19possibilities)
W20 = Point(w20possibilities)
v11correct: y(V11) ≟ v11actual
v12correct: y(V12) ≟ v12actual
v13correct: y(V13) ≟ v13actual
v14correct: y(V14) ≟ v14actual
v15correct: y(V15) ≟ v15actual
v16correct: y(V16) ≟ v16actual
v17correct: y(V17) ≟ v17actual
v18correct: y(V18) ≟ v18actual
v19correct: y(V19) ≟ v19actual
v20correct: y(V20) ≟ v20actual
w11correct: y(W11) ≟ w11actual
w12correct: y(W12) ≟ w12actual
w13correct: y(W13) ≟ w13actual
w14correct: y(W14) ≟ w14actual
w15correct: y(W15) ≟ w15actual
w16correct: y(W16) ≟ w16actual
w17correct: y(W17) ≟ w17actual
w18correct: y(W18) ≟ w18actual
w19correct: y(W19) ≟ w19actual
w20correct: y(W20) ≟ w20actual
b = PolyLine(W0, W1, W2, W3, W4, W5, W6, W7, W8, W9, W10, W11, W12, W13, W14, W15, W16, W17, W18, W19, W20)
V29 = 0
c = PolyLine(V0, V1, V2, V3, V4, V5, V6, V7, V8, V9, V10, V11, V12, V13, V14, V15, V16, V17, V18, V19, V20)