Further examples of harmonic oscillation

[Analog_Engine.git] / scripts / EP1 10.03 Coupled Pendulums.LACE

# 2 coupled pendulums
# x1'' = -k1*x1 + k*(x2-x1)
# x2'' = -k2*x2 - k*(x2-x1)
# xi are the displacement of the pendulum to its resting position

coefficient.1 -> k1
coefficient.2 -> k2
coefficient.3 -> k
coefficient.5(-1) -> -x10 # initial displacement x1
coefficient.6(-1) -> -x20 # initial displacement x2

iintegrate x1'' -> -x1'
iintegrate -x1' -> x1
  IC: -x10

iintegrate x2'' -> -x2'
iintegrate -x2' -> x2
  IC: -x20

cmultiply x1, k1 -> k1*x1
cmultiply x2, k2 -> k2*x2

invert x1 -> -x1
isum x2, -x1 -> -(x2-x1)
cmultiply -(x2-x1), k -> -k*(x2-x1)

isum k1*x1, -k*(x2-x1) -> -k1*x1+k*(x2-x1)
assign -k1*x1+k*(x2-x1) -> x1''
invert -k*(x2-x1) -> k*(x2-x1)
isum k2*x2, k*(x2-x1) -> -k2*x2-k*(x2-x1)
assign -k2*x2-k*(x2-x1) -> x2''

output x1 -> out.x
output x2 -> out.y