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Ecuaciones de Euler-Lagrange péndulo doble con resortes
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  • Course
  • Mecánica y ondas
  • Institution
  • Universidad Europea De Madrid (UEM)

En este documento se consigue las posiciones y velocidades en cartesianas, energía cinética, potencial, Lagrangiano, y ecuaciones de Euler-Lagrange resueltas para un péndulo doble con resortes.

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Document information

  • November 15, 2024
  • 3
  • 2024/2025
  • Other
  • Unknown

Subjects

  • làtex
  • mathematica
  • física
  • péndulo doble
  • resortes
  • lagrangiano
  • ecuaciones de euler lagrange

Written for

  • Universidad Europea de Madrid (UEM)
  • Física
  • Mecánica y ondas
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PÉNDULO DOBLE CON RESORTES
Ernest T.F
Noviembre 2024


1 Posiciones y velocidades del movimiento del
péndulo doble con resortes
Posiciones del péndulo doble con resortes (cartesianas), (decimos que el punto
(0,0) es donde inicia el péndulo):


x1 = l1 sin(θ1 ),
y1 = −l1 cos(θ1 ),
x2 = x1 + l2 sin(θ2 ),
y2 = y1 − l2 cos(θ2 ).


Velocidades del péndulo doble con resortes:
ẋ1 = l˙1 sin(θ1 ) + l1 θ̇1 cos(θ1 ),
ẏ1 = −l˙1 cos(θ1 ) + l1 θ̇1 sin(θ1 ),
ẋ2 = ẋ1 + l˙2 sin(θ2 ) + l2 θ̇2 cos(θ2 ),
ẏ2 = ẏ1 − l˙2 cos(θ2 ) + l2 θ̇2 sin(θ2 ).




Potencial(V) y energı́a cinética(T) (expresiones)
1
m ẋ21 + ẏ12 + ẋ22 + ẏ22 ,

T =
2
1 2 1 2
V = k1 (l1 − L1 ) + k2 (l2 − L2 ) + mg(y1 + y2 ).
2 2
Caso particular para simplificar: k1 = k2 = k, y L2 = L1 = L (longitud
en equilibrio de los resortes):
1  2 2

V = k (l1 − L) + (l2 − L) + mg(y1 + y2 ).
2

1

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