Chapter 55 Forcing and resonance

This chapter is planned for academic year 2022-2023.

maybe return to the cruise control stability problem, putting in disturbances from the car in front.

55.1 Car following dynamics

# random forcing of unit variance
Pts <- tibble::tibble(
  t = seq(0,1000, by=0.5),
  y = rnorm(length(t))
)
random_forcing <- spliner(y ~ t, data = Pts)
slice_plot(random_forcing(t/5) ~ t, domain(t=0:100))

traj <- integrateODE(
  dx ~ -r*(x-x0) -(v - (vf+3*random_forcing(t/8))), 
  dv ~ b*(x-x0),
  dtime ~ 1,
  vf = 100, # feet/second
  x0 = 150, # feet
  b = .25,  # per second,
  r = .5,    # damping
  x = 125,
  v = 110,
  time = 0,
  tdur = list(to=300, dt=0.01))
traj_plot(v(t) ~ t, traj, domain=domain(t=0:300))