meca5.py

Created by martin-tilloy5

Created on March 15, 2024

1.31 KB


# Type your text hereMoment cinetique :
  Moment cinetique d un point / point materiel
  L0 = OM^(mv)
  
  Moment cinetique / axe orienté
  Ldelta = L0(M).udelta
  
  Moment cinetique solide / axe orienté
  Ldelta = Jdelta.w
  Jdelta = mr**2

Moment d'une force / axe orienté :
  Mo(F) = OM^F en Nm
  Mdelta(F) = [OM^F].udelta
  
  Notion de bars de levier
  Mdelta(F) = +ou- F.d avec d le bras de levier
  
  Notion de couple
  F1+F2 = 0
  Mdelata(F1) + Mdelta(F2) = gamma != 0
  moteur si Mdelta = Gamma > 0
  frein si Mdelta = -Gamma < 0 ou = -lambda.w si proportionnel a v angulaire

LMC :
  Point materiel M
  SumMo(Fk) = dL0/dt
  
  Systeme mecanique
  SumMo(Fext) = dL0/dt
  SumMdelta(Fext) = dLdelta/dt = Jdelta.wpoint = Jdelta.ThetaPointpoint

Pendule :
  Pendule de torsion 
  Mdelta = Gamma(t) = -CTheta
  ThetaPointpoint + Omega0**2.Theta = 0
  Omega0 = sqrt(C/Jdelta)
  E = 1/2.Jdelta.w**2 + 1/2.C.Theta**2
  
  Energie cinetique en rotation : 
    E = 1/2.Jdelta.w**2
    
    Pour un solide en rotation : 
      Ecb - Eca = 1/2.Jdelta.w**2(a) - 1/2.Jdelta.w**2(b) = SumWab(Fext)
    
    Pour un sollide deformable : 
      (Jdelta + 2mr**2).w1 = (Jdelta + 2mR**2).w2
      
  Energie potentielle de torsion : 
    E = 1/2.Jdelta.C.Theta**2
  
  Pendule pesant :
    ThetaPoinpoint + mga/Jdelta * sin(Theta) = 0

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