File:Pendule de Foucault-vitesse nulle.png

# Gnuplot programme foucault.gp
g=9.81 #m/s2
l=63   # mètres
omega=sqrt(g/l)
Omega=2*pi/24/3600 # Rotation de la terre, 24 heures par jour
Omega=2*pi/3600*80 # Rotation très rapide en 1/80e d'heure pour le dessin
print 2*pi/Omega

theta=pi/4.  # latitude de 45 degrés
omegz=sqrt(omega*omega+Omega*Omega*sin(theta)*sin(theta))

complex(x,y)=x*{1,0}+y*{0,1} # fonction utile

# cas où le pendule est propulsé du centre avec une vitesse de 2m/s
z0={0,0}
vz=2         # Si propulsé au centre avec une vitesse de 2 m/s
zp0=complex(vz,0)

# cas 'historique' où le pendule est lancé sans vitesse
#   initiale à 5 m du centre.
z0={5,0}
zp0={0,0}
print zp0

c1=z0/2.*(1+Omega/omegz*sin(theta))*{1,0}-zp0/2./omegz*{0,1}
c2=z0/2.*(1-Omega/omegz*sin(theta))*{1,0}+zp0/2./omegz*{0,1}

eix(x)=cos(x)*{1,0}+sin(x)*{0,1}
z(t)=c1*eix(-(Omega*sin(theta)-omegz)*t) + c2*eix(-(Omega*sin(theta)+omegz)*t)
set samples 1000
set parametric
plot [t=0:2*pi/Omega/sin(theta)] real(z(t)),imag(z(t))
# replot abs(z0)*cos(t),abs(z0)*sin(t)
set ter png
set out "foucault-vitesse-nulle.png"
replot

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