jsMath

Tractrix_Evolute

1 second ago by admin

var('t') a(t)= (1/cosh(t),t-tanh(t)) parametric_plot( a(t), (t, 0, pi), color = 'red') 
       
a1=derivative(a,t) a2=derivative(a1,t) 
       

k=((a1[0]*a2[1] - a2[0]*a1[1])/((a1.norm())^3)) T=a1/(a1.norm()) T1=derivative(T,t) KV=(T1/(a1.norm())) beta=a+( KV/(k^2 )) 
       

plotCurve = parametric_plot( a(t), (t, 0, pi/2),thickness=3, color='red'); plotEvolute = parametric_plot( beta(t), (t,0, pi/2), color='grey'); plot([plotCurve, plotEvolute]) 
       
var('s') r(s,t)=((1/k)*cos(s), (1/k)*sin(s)) c=beta+r plotCircles = [parametric_plot( c(s,t), (s, 0, 2*pi), rgbcolor=(1-2*t/pi,1,2*t/pi))for t in [0.1..pi/2,step=0.2]] ; plot([ plotCircles,plotCurve, plotEvolute],aspect_ratio=1)