formules.py

Created on March 10, 2022
1008 Bytes
from math import *

Légende :
d(f) = variation(f)
\v   = vecteur v
k    = constante

#--------------------------------
Energies

Ec = 1/2 * m * v2
Epp = m * g * h
Em = Ec + Epp

Si on néglige les forces non-conservatives :
d(Em) = 0 <=> Em est constante
Sinon,
d(Em) = W(f) (forces non-conservatives)

W(P) = m*g*(za-zb)
W(Elec) = q*U = q(Va-Vb)

#--------------------------------
Particule champs électrique

\a = +-q/m * \E

     e-     e
+ |-----|------|
- |  +  |   -  |
  |-----|------|
- |  -  |   +  |
+ |-----|------|

Dans (o,i,j): 
  ax = 0
  ay = +-q/m*0E

#-----------------------------
Mouvement champs gravitationel

3 lois de kepler
1 : héliocentrique => orbite = ellipse, soleil = foyer
2 : Lois des aires
3 : T^2 / r^3 = 4*pi^2 / G*M = k

F = G * (m1 * m2) / d^2 
\F = F*\n

accélération :
  \a * mS = \F => \a = G * mT / r^2 * \n
vitesse : 
  v^2 / r = GmT/r^2 => v = sqrt(GmT/r)
période :
  T = (2*pi*r)/v
  T = (2*pi*r)/sqrt(GmT/r)
  T = 2*pi*sqrt(r^3/G*mT)