x 2 1 2 m x 2 \u2113 2 \u03b8 2 2 x \u2113 \u03b8 cos\u03b8 mg\u2113 mg\u2113 cos \u03b8 kx 2 T 1 2M x 2 1 2 m x2 \u2113 2 \u03b8

X 2 1 2 m x 2 ℓ 2 θ 2 2 x ℓ θ cosθ mgℓ mgℓ

This preview shows page 19 - 29 out of 33 pages.

x 2 + 1 2 m ! x 2 + 2 ! θ 2 + 2 x ! θ cos θ ( ) + mg mg cos θ kx 2 T = 1 2 M ! x 2 + 1 2 m ! x 2 + 2 ! θ 2 + 2 ! x ! θ cos θ ( ) mg 1 cos θ ( ) V = 1 2 kx 2 + 1 2 k x ( ) 2 L = T V
Image of page 19
Mécanique analytique : Exercice 2 1 ère équation du mouvement : M + m ( ) !! x + 2 kx + 2 !! θ cos θ m ! θ 2 sin θ = 0 d dt L ! x L x = 0 Équation de Lagrange pour le degré de liberté : m 2 "" θ + ℓ"" x cos θ ( ) + mg sin θ = 0 0 = θ θ L L dt d ! 2 ème équation du mouvement : Équation de Lagrange pour le degré de liberté : x θ
Image of page 20
Mécanique analytique : Exercice 2 M + m ( ) !! x + 2 kx + 2 !! θ cos θ m ! θ 2 sin θ = 0 m 2 "" θ + ℓ"" x cos θ ( ) + mg sin θ = 0
Image of page 21
MOOC Introduction à la Physique Quantique Exercice guidé du Chapitre 2 Transparents de la vidéo 2.C Frédérika Augé-Rochereau
Image of page 22
x y z ! r α t ( ) Mécanique analytique : Exercice 2 ! E = ! U ! A t N particules m α = 1,..., N , e α = 1,..., N , ! r α = 1,..., N ! B = ! ∇× ! A
Image of page 23
x y z ! r α t ( ) Mécanique analytique : Exercice 2 L = 1 2 m α ! " r α ! " r α ( ) + e α ! " r α " A e α U " r α ( ) α = 1 N N particules m α = 1,..., N , e α = 1,..., N , ! r α = 1,..., N
Image of page 24
Mécanique analytique : Exercice 2 L = 1 2 m α ! " r α ! " r α ( ) + e α ! " r α " A e α U " r α ( ) α = 1 N p α L ! " r α = m α ! " r α + e α " A " r α , t ( ) ! " r α = " p α e α " A " r α , t ( ) m α
Image of page 25
Mécanique analytique : Exercice 2 = m α ! " r α + e α " A " r α , t ( ) ( ) ! " r α 1 2 m α ! " r α ! " r α ( ) e α ! " r α " A " r α , t ( ) + e α U " r α ( ) α = 1 N H = ! p α " ! r α α = 1 N L = ! p α e α ! A ! r α , t ( ) ( ) 2 2 m α + e α U ! r α ( ) α = 1 N = 1 2 m α ! " r α ! " r α ( ) + e α U " r α ( ) α = 1 N
Image of page 26
Mécanique analytique : Exercice 2 ! " p α = H " r α ! " r α = + H " p α H = ! p α e α ! A ! r α , t ( ) ( ) 2 2 m α + e α U ! r α ( ) α = 1 N α 1,..., N { }
Image of page 27
Mécanique analytique : Exercice 2 α 1,..., N { } !
Image of page 28
Image of page 29

You've reached the end of your free preview.

Want to read all 33 pages?

  • Fall '19
  • mécanique quantique, Pesanteur, Équations de Lagrange, Mécanique analytique

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

Stuck? We have tutors online 24/7 who can help you get unstuck.
A+ icon
Ask Expert Tutors You can ask You can ask You can ask (will expire )
Answers in as fast as 15 minutes