Référentiels en mécanique classique

O
(Ox, Oy, Oz)
(x, y, z)
(−→ ux,−→ uy,−→ uy)

M
R
M
t
P(t)M t
R t P (t+∆t)
t+ ∆t t R
−→
vM/R = lim
∆t→0
−−−−−−−−−−→
P(t)P(t+ ∆t)
∆t=d−−→
OM
dt
−−→
OM R
(x(t), y(t), z(t)) O
−−→
OM(t) = x(t)−→ ux+y(t)−→ uy+z(t)−→ uz
M R
R
−→
vM/R =d−−→
OM
dt =dx dt −→
ux+dy
dt −→
uy+dz
dt −→
uz
−→
aM/R =d−→
vM/R
dt =d2x dt2−→
ux+d2y
dt2−→
uy+d2z
dt2−→
uz
O
r ω Oxy
−−→
OM =rcos(ω t)−→ ux+rsin(ω t)−→ uy

(−→ ur,−→ uθ)
−−→
OM =r−→ ur
−→
v=rω−→ uθ
−→
a=−rω2−→ ur
R
R0
R0R
O0R0R0
P R0O0
−→
vP/R(t) = −→ vO0/R(t)
Référentiel R
R'
O'
P
A B R0
d−→ AB
dt =−→
0

R0R
R0
d−→ ux0
dt =−→
0
O0R
O0R
30 km/s
10000
M R
R0M R
R0
R R0
−−→
OM =−−→ OO0+−−→ O0M
O R O0R0
R−−→ O0M R
R0
d−−→ O0M
dt =d dt (x0(t)−→
ux0+y0(t)−→ uy0+z0(t)−→ uz0)
=dx0(t)
dt −→
ux0+dy0(t)
dt −→
uy0+dz0(t)
dt −→
uz0
R0
M R0
−→
vM/R =−→ vO0/R +−→ vM/R0

R0
O0R0
R P R0M t
−→
vM/R =−→ ve+−→ vM/R0
−→
aM/R =−→ aO0/R +−→ aM/R0
O0
R R0M t
c
R0
R
−→
vO0/R =v−→ ux
(O0x0y0z)R0t= 0
(Oxyz)R
x0=x−vt
y0=y
z0=z
t0=t
v
x0=x−vt
√1−v2/c2
y0=y
z0=z
t0=t−vx/c2
√1−v2/c2