lagrange.py

Created on October 21, 2023

596 Bytes

qi : systènes de variables des coordonnées 
Lagrangien 
L= Ec + Ep
Equation de Lagrange (non conservatif) : 
  d(drond L/drondqi')/dt - drond L/ drond qi = 0 ( + Gammai, force ne résultant pas d'un potentiel)
Soit avec deux variables de coordonnées, deux équations
Puis résolution matricielle 
[M]q" + [C]q' + [K][q] = {f}
M matrice d'inertie K matrice de rigidité
on recherche alors des pulsations propres naturelles:
  {q"} + w2{q} =0
Il faut donc résoudre :
  det ([k]-w2[M])
Sinon si on recherche les valeurs propres :
  det [K^ -w2I] = 0
  avec K^= M^-1/2 K M^-1/2

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lagrange.py