Référentiels non galiléens Notes de cours - Alain Le Rille

R
m~a/R(M) = X~ f→M
1 an
24 h
R0R R0
R0R M R R0
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•R
(O, ~ux, ~uy, ~uz)
•R0
(O0, ~ux0, ~uy0, ~uz0)
R0
R
~ux0=~ux
~uy0=~uy
~uz0=~uz
M
•−−→ OM (t) = x(t)~ux+y(t)~uy+z(t)~uz
R
•−−−→ O0M(t) = x0(t)~ux+y0(t)~uy+z0(t)~uz
R0
~v/R(M)M R ~v/R0(M)M
R0
~v/R(M) = ~v/R0(M) + ~ve
~veR0R
P M t R0
R0R
M t P
~ve=~v/R(P)
t0P M
P0
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~a/R(M)M R ~a/R0(M)M
R0
~a/R(M) = ~a/R0(M) + ~ae
~aeR0R
R0~ F
~
fie =−m.~ae
R0R
~ve(M) = ~v0=−−→ cste
~v/R(M) = ~v/R0(M) + ~v0
R0R
~ae=a0~ux
Ep=m a0x
R0
R ~ve= +v(t)~ux~ae=−a ~ux
R0R0
R ~ve= +v0~uθ~ae=−v2
0
R0~ur
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◦

•R
(O, ~ux, ~uy, ~uz)
•R0
(O0, ~ux0, ~uy0, ~uz0)
R0
R
O0O ~uz0=~uz
~
Ω=Ωz~uzΩz=dθ
dt
M
•−−→ OM =x ~ux+y ~uy+z ~uzR
•−−−→ O0M=x0~ux0+y0~uy0+z ~uzR0
~v/R(M)M R ~v/R0(M)M
R0
~v/R(M) = ~v/R0(M) + ~ve
~ve
~a/R(M)M R ~a/R0(M)M
R0
~a/R(M) = ~a/R0+~ae+~aC(M)
~aC= 2.~ ΩR0/R ∧~v/R0(M)
~ae=~a/R(P)
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