Rapport de projet tutoré - Le nouveau pendule chaotique

m l θ
~g
m
θ
~ex~g
x
z
~ez
~er
~eθ
l
x=lsin θ
y= 0
z=−lcos θ
⇒
˙x=l˙ θcos θ
˙z=l˙ θsin θ

Ec=1
2mv2=1 2mp˙x2+ ˙y2+ ˙z22
=1
2ml2˙
θ2
Ep=−~ P·~r =mgz =−mgl cos θ
L=Ec−Ep=1
2ml2˙
θ2+mgl cos θ
∂L
∂θ =d dt
∂L
∂˙ θ
⇒¨ θ=−g
lsin θ
ϕ ~ex

m
x
z
~ex~g
~ey
~ez
~er
~eθ
~eφ
l
θ
ϕ
∂L
∂θ =d dt
∂L
∂˙ θ
⇒¨ θ= ˙ϕ2sin θcos θ−g
lsin θ
∂L
∂ϕ =d dt
∂L
∂˙ϕ⇒¨ϕ=−2˙
θ˙ϕcot θ