(* Ball rolling on a cosine curve.                          *)
(* Illustrates the impact of an observer on the simulation. *)

let g  = 9.81
let mu = 0.5  (* Friction coefficient. *)

let hybrid ball(v0) = (x, v) where
  rec der x = v init 0.0
  and der v = a *. (cos x) init v0
  and     a = g *. (sin x) -. mu *. v /. (cos x)

let hybrid vdp_c(mu) = (x, y) where
  rec der x = y init 1.0
  and der y = (mu *. (1.0 -. (x *. x)) *. y) -. x init 1.0

let hybrid print(p)(t, x, v, x', y) = () where
  present(period(p)) -> do
    () = print_endline(String.concat ",\t\t" (List.map string_of_float [t;x;v;x';y]))
  done

(* Changing the period for [print] changes the result. *)
let hybrid main () = () where
  rec der t  = 1.0 init 0.0
  and (x, v) = ball(2.953)
  and (x', y) = vdp_c(0.5)
  and ()     = print(0.5)(t, x, v, x', y)

(*
let input _ = 2.953

let node print_discrete (now, (x, v)) =
  print_endline (String.concat ",\t\t" (List.map string_of_float [now;x;v]))

let ball_discrete = Solve.solve_sundials(ball)

let node main_discrete () =
  let input = Some (Solve.make(30.0, input)) fby None in
  let o = run ball_discrete input in
  Solve.period'_t 1.0 print_discrete o
*)