Class DoublePendulumSim

Simulation of a double pendulum.

Variables and Parameters

Variables:

th1, th2 = angles of sticks with vertical; down = 0; in radians;
           counter-clockwise is positive
dth1, dth2 = angular velocities; first derivative with respect to time of th1, th2

Parameters:

L1, L2 = stick lengths
m1, m2 = masses
g = gravity

This diagram shows how the sticks and masses are connected:

        \
         \L1
          \
           m1
           |
           |L2
           |
           m2

Equations of Motion

The derivation of the equations of motion is shown at https://www.myphysicslab.com/pendulum/double-pendulum-en.html. See also the [Double Pendulum Mathematica notebook(../Double_Pendulum.pdf) which uses an algebra solver to find the above equations.

        -g (2 m1 + m2) Sin[th1]
        - g m2 Sin[th1 - 2 th2]
        - 2 m2 dth2^2 L2 Sin[th1 - th2]
        - m2 dth1^2 L1 Sin[2(th1 - th2)]
ddth1 = ------------------------------------
        L1 (2 m1 + m2 - m2 Cos[2(th1-th2)])

        2 Sin[th1-th2](
          (m1+m2) dth1^2 L1
          + g (m1+m2) Cos[th1]
          + m2 dth2^2 L2 Cos[th1-th2]
        )
ddth2 = ------------------------------------
        L2 (2 m1 + m2 - m2 Cos[2(th1-th2)])

Variables Array

The variables are stored in the VarsList as follows

vars[0] = th1
vars[1] = th1'
vars[2] = th2
vars[3] = th2'
vars[4] = th1''
vars[5] = th2''
vars[6] = kinetic energy
vars[7] = potential energy
vars[8] = total energy
vars[9] = time

TO DO add damping force.

TO DO add ParameterBoolean specifying whether to limit angles to +/-Pi.

Hierarchy (view full)

Implements

Constructors

constructor

Properties

initialState_

Methods

addObserver addParameter broadcast broadcastParameter evaluate finishDrag getBroadcast getClassName getEnergyInfo getGravity getMass1 getMass2 getName getObservers getPEOffset getParameter getParameterBoolean getParameterNumber getParameterString getParameters getRod1Length getRod2Length getSimList getTime getVarsList handleKeyEvent modifyObjects mouseDrag moveObjects removeObserver removeParameter reset restState restoreState saveInitialState saveState setBroadcast setGravity setMass1 setMass2 setPEOffset setRod1Length setRod2Length setTerminal setVarsList startDrag toString toStringShort

Constructors

constructor

Properties

Protected initialState_

initialState_: null | number[] = null

Initial values.

Methods

addObserver

  • addObserver(observer): void

  • Adds the given Observer to this Subject's list of Observers, so that the Observer will be notified of changes in this Subject. An Observer may call Subject.addObserver during its observe method.

    Parameters

    Returns void

addParameter

broadcast

broadcastParameter

evaluate

  • evaluate(vars, change, _timeStep): null | object

  • Defines the differential equations of this ODESim; for an input set of variables, returns the current rate of change for each variable (the first derivative of each variable with respect to time).

    The timeStep is the time since the state variables were last fully calculated, which can be and often is zero. The current time can be regarded as getTime() + timeStep. The input variables correspond to the Simulation state at that time. Note that timeStep is different from the time step used to advance the Simulation (as in AdvanceStrategy.advance). The timeStep is typically used when finding collisions in CollisionSim.findCollisions.

    Parameters

    • vars: number[]

      the current array of state variables (input), corresponding to the state at getTime() + timeStep

    • change: number[]

      array of change rates for each variable (output), all values are zero on entry.

    • _timeStep: number

      the current time step (might be zero)

    Returns null | object

    null if the evaluation succeeds, otherwise an object relating to the error that occurred. The change array contains the output results.

finishDrag

  • finishDrag(_simObject, _location, _offset): void

  • Called at the end of a mouse drag operation, performs whatever action is appropriate. Only called if startDrag returned true.

    Parameters

    • _simObject: null | SimObject

      the SimObject being dragged, or null if no SimObject was found

    • _location: Vector

      the location of the mouse in simulation coordinates of the SimView where simObject was found, or in the focus view if simObject is null.

    • _offset: Vector

      distance from the initial object position to the mouse location at start of drag.

    Returns void

Protected getBroadcast

getClassName

getEnergyInfo

getGravity

getMass1

getMass2

getName

getObservers

getPEOffset

getParameter

getParameterBoolean

getParameterNumber

getParameterString

getParameters

getRod1Length

getRod2Length

getSimList

getTime

getVarsList

handleKeyEvent

  • handleKeyEvent(_evt, _pressed, _modifiers): void

  • Called when a key is pressed or released, performs whatever action is appropriate for that event.

    Parameters

    • _evt: KeyboardEvent

      the KeyboardEvent that happened

    • _pressed: boolean

      true means this is a key-down event; false means a key-up event

    • _modifiers: ModifierKeys

      the modifier keys down during event

    Returns void

modifyObjects

mouseDrag

  • mouseDrag(simObject, location, offset): void

  • Called at each movement during a mouse drag, performs whatever action is appropriate. Only called if startDrag returned true. The SimObject being moved is passed in, along with the current mouse position, in simulation coordinates, and an offset calculated at the start of the drag.

    Setting the SimObject position to (x - offsetX, y - offsetY) will move the SimObject smoothly along with the mouse movement.

    Parameters

    • simObject: null | SimObject

      the SimObject being dragged, or null if no SimObject was found

    • location: Vector

      the location of the mouse in simulation coordinates of the SimView where simObject was found, or in the focus view if simObject is null.

    • offset: Vector

      distance from the initial object position (from DisplayObject.getPosition) to the mouse location at start of drag.

    Returns void

Private moveObjects

removeObserver

removeParameter

reset

restState

restoreState

saveInitialState

saveState

Protected setBroadcast

  • setBroadcast(value): boolean

  • Sets whether this Subject will broadcast events, typically used to temporarily disable broadcasting. Intended to be used in situations where a subclass overrides a method that broadcasts an event. This allows the subclass to prevent the superclass broadcasting that event, so that the subclass can broadcast the event when the method is completed.

    Parameters

    • value: boolean

      whether this Subject should broadcast events

    Returns boolean

    the previous value

setGravity

setMass1

setMass2

setPEOffset

setRod1Length

setRod2Length

setTerminal

Protected setVarsList

startDrag

  • startDrag(simObject, _location, _offset, _dragBody, _modifiers): boolean

  • Called at the start of a mouse drag. The nearest dragable SimObject is passed in, along with mouse position in simulation coordinates. If no dragable SimObject was found, null is passed for the first argument. If the EventHandler does not recognize the SimObject then it should return false.

    Parameters

    • simObject: null | SimObject

      the SimObject that is nearest to the mouse drag coordinates, or null if no SimObject was found

    • _location: Vector

      the location of the mouse in simulation coordinates of the SimView where simObject was found, or in the focus view if simObject is null.

    • _offset: Vector

      distance from the initial object position (from DisplayObject.getPosition) to the mouse location at start of drag

    • _dragBody: null | Vector

      location of 'drag point' on the SimObject in body coordinates of the SimObject; this is where for example a spring will be attached on the SimObject when dragging; or null when no SimObject was found

    • _modifiers: ModifierKeys

      the modifier keys down during event

    Returns boolean

    true if the EventHandler will handle dragging the SimObject

toString

toStringShort

  • toStringShort(): string

  • Returns a minimal string representation of this object, usually giving just identity information like the class name and name of the object.

    For an object whose main purpose is to represent another Printable object, it is recommended to include the result of calling toStringShort on that other object. For example, calling toStringShort() on a DisplayShape might return something like this:

    DisplayShape{polygon:Polygon{'chain3'}}

    Returns string

    a minimal string representation of this object.

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