Chapitre 10 :Dynamique dans des référentiels non galiléens
Transcription
Chapitre 10 :Dynamique dans des référentiels non galiléens
T his work is licensed under a Creative Commons “Attribution-ShareAlike 4.0 International” license. ! " " # $ ! # • % ) +& ! & '& ( = ** # " + +& ( ' & ( +& & ' ** = & ( +& & ! % , & ( ' ! = & ( +& − = +& ! " " • & # & .& ( & = " & ( #- = ( +& # ' #$ / " 0 ! & ( = ( +& & # #-' # " ' &/ # &/ ) ' & " 1 1 ) #% & " = & ' ' 3' 2 ' & ( = & (' ' 3' 2 & ( # Ismaël Bouya http://melusine.eu.org/syracuse/immae/ ) " = (+ ( = (= + × ( +& + ( (& ) " +& = +& ( + +& = +& ( + ( +& ) + ( +& " +& ( = = 4 = 1 / . = # & +& -' ' & ( = # +& = +& ( # +& ( $ " # " " , 5 # / " 6 & " " / 7 8 # & - 7 & % '& # . # ) = +& + +& & + +& / . # +& = - +& ⇔ + +& + =− ( =− ( = + = ⇔ & +& = − + ( + 4 . / % 3 . < = ' +& ( =4 ( & + + : ( & - ' (= (= (= ; = +4 ( & : # ( +4 ( & . & & (' (' ( < & = + $ 0 ) = 7 % σ ! & = +& σ # ∧ +& = +& ∧ & + +& ∧ +& & & = = σ ∧ +& = +& ∧& + = +& + + & + & & & ) 7 & +& = 4 +& 4 +& = (4 4 = # +& # +& +& ) +& # & = +& =δ & #& + + +δ & & +δ & .& 'δ & = &−4 ω ∧ =− +& # = +& δ & = = # 9 'δ & - = & < 8 ' +& +& - ∆ +& =δ & +δ & = & + & = + & & 6! ) %& .& =− & > ( +& ! & = 4 / ! ! %& ! = ω4 & > = −4 ω ∧ δ & = = ω 3 & ω = ω& +& = # 4 ! # ! +& + # .& # + ω 4 # =− − ω4 = ⊥ ++ 4 = ω 4 4 4 4 " " =− 4 ! ! # ω4ρ 4 ρ = −4 ω ∧ / +& " # = 6 7 $ - & 7 . 3 = + +& & & + 7 . − = +& +& + < ! - < " & . # 0 / & < ) # , << << 4= = @= 2 / .& & & =& Ω = ω& ' +& ' =Ω " & Ω= 4π 49 ?@ = " << = B'4A# −? # ; << # # = '?# ? / & &C = & (' ' ' ! D , & > ' ' ' & & & # " / " < . & 2 " & #& AAE D , & 9@?'4?3# 7 < ' 7 7 << . # << 4? # @ 7 !" # $% - # - & " # & - < = . & & . < < = Ω4 @ 6 ⇔ < $ =− = ' " = " − − = & 4 = & = < # = + Ω4 4 = + + ' " 4 " + . − = " + Ω4 " + Ω4 = # = + Ω4 " ' # Ω4 AA'?E . # " ≈ 9# & " # ;9 #6 7 ! ' # $ ≤ & # 2 ' , # ' ! + < ' 0 + = ⇔ + ' ' = & - ! " " 7 . ' " ' ' & " B / . = +& + + " & + = +& = + " + " 7 Ω = Ω ++ + Ω ⊥ - " " # = −4 Ω ∧ ⊥ = −4 Ω ⊥ ∧ $ # ' Ω 7 ' " # ' # F 4 " " λ & " " ' ' " ' 7 / 7 + = & ' ' " Gλ . = ' " . = & +& +& = −4 Ω ∧ - +& λ λ ΩΩ Ω = −4 Ω Ω = λ∧ λ λ− λ λ = −4 Ω − λ =− / = 4 Ω& λ− = −4 Ω λ =− +4 Ω Ω ; $ - λ = 4Ω& λ− = −4Ω λ = − + 4Ω λ ⇔ λ 7 λ Ω# = = = = = = =− =− # = !− " 4 # 4 ' = 4! A ; $ Ω . λ = 4Ω =Ω # = λ 4 + Ω # 9 = = = =− =− # = !− 4! = = Ω # 9 4 λ> 9 " ! 4 λ & − != != # 9 ; ∆ = '? ∆ = '=A " # λ =? ° & & 6 & &" # 0 → = − G 4 - = "→ − " " 4 ( 7 7 " < #$ " 4 7 3 # 0 6 - & .& #- # $ = G ( = " " ' & → = . − G 4 =− =− = "→ − " 4 " ( +& / . = +& "→ = +& 6 "→ = " " " " " " 4 " − < 4 " & + =− − → " " " 4 " + + + "→ " 4 " " " # ' " = = = +& > = − " × ∈ &" " 4 − " 4 " " ) &
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