sujet - banques

???
•
1
p1 + η2−2ηx =
∞
X
n=0
ηnPn(x)
η∈[−1,1] x∈[−1,1] Pn(x)
P0(x)=1
P1(x) = x
P2(x) = (3x2−1)/2
P3(x) = (5x3−3x)/2
P4(x) = . . .
•~ A
~
rot ( ~ rot ~ A) = ~ grad (div ~ A)−∆~ A
•
me= 9,11 ×10−31 kg
mp= 1,67 ×10−27 kg
−e=−1,60 ×10−19 C
~= 1,05 ×10−34 J.s
G= 6,674 ×10−11 m3.kg−1.s−2
g= 9,8 m.s−2
0= 8,85 ×10−12 kg−1.m−3.A2.s4
c= 2,998 ×108m.s−1
R= 8,314 J.mol−1.K−1

G
e
−e r
memp
~c4π0e α
e2
αg
α
−α2/n2n= 2
n= 1

G
G
m2l
M d
G
θ
k−k θ ~z
M m
θ θ l d
ld
m= 0,80 kg M= 158 kg
l= 1,0 m d= 20 cm k= 3,6×10−4kg.m2.s−2θ
I
G
θ
G M l
d θ
G
T
m l
RT
MTRTM d T θ

G
M R
O V (~r)
~r ~ R
~r r < R γ ~r ~ R
V(~r)
V(~r) = V(γ, r) = −
∞
X
n=0
an(γ)rn
Rn+1
an(γ)M G γ
Pn(−x)=(−1)nPn(x)
γ
V(γ, r) = V0(r)−(3G/2)Q r2cos2γ V0(r)γ Q
M
Ep(φ) = E0−(3G/2)q Q cos2φ q
E0φ
G q
Q φ
q

ω(t) = ω0+δω(t)ω0δω(t)
δω(t)R0= (O, x0, y,0z)
ω(t) (O, z)
(O, x, y, z)R0
Moteur
θ R0
~
Fe~ FcR0
~ae~ω =ω ~z ~v R0
~ae
(~ur, ~uθ)~ Fe~ Fc
˙ω(t)
θ(t)φ(t)
˙ω(t)I G q Q I
θ= 0
δω(t)φ(0) = 0
ε=GQq/(Iω2
0)
ε δω(t)
δω(t)
ε
δω(t) = δω0cos ωmt δω0ωmω0q Q I
G
δω0G G
ω0δω0I q Q M R
G I q Q
M m
q/I
G
Q