Pendule en référentiel non galiléen

G
g
L
a
b
θ
Moteur
Bâti
Chariot
Bielle
x
y
O
A
B
α
β
L θ
O
a=OA b =AB
B(x, h)
Ox α =ωt ω
β
−→
OA −→ AB
x=acos α+bcos β
h=asin α+bsin β
h
β

x=acos α+pb2−(h−asin α)2
x(t)
h= 0 b2a2

x=b+acos α=b+acos(ω t)
ae=d2x
dt2=−aω2cos(ω t)
G
m
J
Jd2θ
dt2+νdθ dt +mgL sin θ=Lmaω2cos θcos(ωt)
ν
θ(0) ˙ θ(0)
Jd2θ
dt2+νdθ dt +mgLθ =Lmaω2cos(ωt)
J
ω0=rmgL
J
ω= 0 T
t0=t
T=ω0 2πt
t0
1
dt =ω0 2π
1
dt0
1
dt2=ω0 2π21 dt02

d2θ
dt02+2πν Jω0
dθ
dt0+ (2π)2sin θ=Lma J2πω ω02
cos θcos ω
ω0
2π t0
θ t0
T0= 1
γ=2πν
Jω0
A=Lma
J
f=ω
ω0
d2θ
dt02+γdθ dt0+ (2π)2sin θ=A(2π)2f2cos θcos (2π f t0)
va
dθ
dt0=va
dva
dt0=−γva−(2π)2sin θ−A(2π)2f2cos θcos(2π f t)