How to resolve the algorithm Animate a pendulum step by step in the Elm programming language

Published on 12 May 2024 09:40 PM
#Elm

How to resolve the algorithm Animate a pendulum step by step in the Elm programming language

Table of Contents

Problem Statement

One good way of making an animation is by simulating a physical system and illustrating the variables in that system using a dynamically changing graphical display. The classic such physical system is a simple gravity pendulum.

Create a simple physical model of a pendulum and animate it.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Animate a pendulum step by step in the Elm programming language

Source code in the elm programming language

import Color exposing (..)
import Collage exposing (..)
import Element exposing (..)
import Html exposing (..)
import Time exposing (..)
import Html.App exposing (program)

dt = 0.01
scale = 100

type alias Model =
  { angle : Float
  , angVel : Float
  , length : Float
  , gravity : Float
  }

type Msg 
    = Tick Time

init : (Model,Cmd Msg)
init =
  ( { angle = 3 * pi / 4
    , angVel = 0.0
    , length = 2
    , gravity = -9.81
    }
  , Cmd.none)

update : Msg -> Model -> (Model, Cmd Msg)
update _ model =
  let
    angAcc = -1.0 * (model.gravity / model.length) * sin (model.angle)
    angVel' = model.angVel + angAcc * dt
    angle' = model.angle + angVel' * dt
  in
    ( { model
        | angle = angle'
        , angVel = angVel'
      }
    , Cmd.none )

view : Model -> Html Msg
view model =
  let
    endPoint = ( 0, scale * model.length )
    pendulum =
      group
        [ segment ( 0, 0 ) endPoint
            |> traced { defaultLine | width = 2, color = red }
        , circle 8
            |> filled blue
        , ngon 3 10
            |> filled green
            |> rotate (pi/2)
            |> move endPoint
        ]
  in
    toHtml <|
      collage 700 500
        [ pendulum |> rotate model.angle ]

subscriptions : Model -> Sub Msg
subscriptions _ = 
    Time.every (dt * second) Tick

main =
  program 
      { init = init
      , view = view
      , update = update
      , subscriptions = subscriptions
      }

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