' - - File: XXX1.txt

pi = 3.14159
tx = -1                                                                     ' Value to vary for animation.
R<t> = <2cos[t], sin[t], 0>
T<t> = vTan[R]
Ta{t} = sMag[vDiv[vDiff[T],sMag[vDiff[R]] ]]       ' k{t} = |dT/dt| / (ds/dt) = dT/ds
ra = 1 / Ta{tx}
' - - - - - - - - - - - - - - - - - - - - - - - - - - - - Method #2 - - - - - - - - - - - - - - - - - - - - - - - - - 
Ka<t> = vDiff[R]                              '  dR/dt =R'
Kb<t> = vDiff[R,2]                           '  d(dr/dt)/dt = R"

Kn{t} = sMag[vCross[Ka,Kb]]        '   | R' x R" |
Kc{t} = sMag[Ka]                            '   | R' |
Kd{t} = Kc{t}^3                                '   | R' |^3
Ke{t}= Kn{t} / Kd{t}                         '   | R' x R" |  /  | R' |^3
rb = 1/ Ke{tx}                                  '   ANS: 1/ Ke{t1} = 1.5, same answer as ra above.
   
C<t> =   vAdd[R, vMpy[ra, vNorm[R]]]                  ' C<t> = R<t> + ra * N<t>
hx = C.x | tx  :  hy = C.y | tx

'Cr<t> =<ra * Cos[pi*t] + hx, ra * Sin[pi*t] +hy , 0>

Ea<t> = vAdd[R, vDiv[Ke, vNorm[R]] ]

t0 = -pi  :  tf = pi  :  n = 100
Plot[R, Ea, {t, t0, tf, n}]
<t = tx>           ' Need for work sheet output to verify results.

