parametric
Author: kmassey

tmin

tmax

tanline

accel-components

pva-vectors

f(t) = cos(3 * t)
g(t) = sin(t)
T = 2.72 (slider from tmin to tmax, step 0.01)
tmin = 0
p = CurveCartesian(f(t), g(t), t, tmin, T)
v = Derivative(p)
tmax = 6.283
inputBox1 = Textfield(tmin)
inputBox2 = Textfield(tmax)
A: p(T)
speed(t) = sqrt(Derivative[f]^(2) + Derivative[g]^(2))
Aspeed: speed(T)
start: p(tmin)
showTanline = false
tanline = Tangent(A, p)
odometer = Integral(speed, tmin, T)
text2: "odometer = \int_{tmin}^T speed(t)\ dt = " + (LaTeX[odometer]) + ""
vv = Vector(A, A + v(T))
text1: "speed(T) = " + Aspeed + ""
a = CurveCartesian(f''(t), g''(t), t, tmin, T)
av = Vector(A, A + a(T))
uT = UnitVector(vv)
aT: (av * vv) / Length[vv]
aTT = Vector(A, A + aT * uT)
aN: sqrt(av * av - aT^(2))
aNN = Vector(A, A + av - aTT)
uN = UnitVector(aNN)
kappa: aN / (vv * vv)
RofC: 1 / kappa
aTT2 = Vector(A + aNN, A + av)
aNN2 = Vector(A + aTT, A + av)
oscCirc = Circle(A + RofC * uN, RofC)
pfull = CurveCartesian(x(p(t)), y(p(t)), t, tmin, tmax)
showAccel = false
pv = Vector(p(T))
showPVA = false