Class CollideBlocksSim

Simulation of two blocks moving horizontally between walls, with collisions between the blocks and walls. One of the blocks is connected to a wall with a spring. The order of objects left to right is: left wall, block 1, block 2, right wall.

Variables and Parameters

Origin at right edge of left wall. Variables: text vars[0] = block 1 position vars[1] = block 1 velocity vars[2] = block 2 position vars[3] = block 2 velocity Parameters: text R = rest length S1 = left end of spring S2 = right end of spring (same as x?) len = current length of spring = x - S1.getX() L = how much spring is stretched from rest length L = len - R = x - S1.getX() - R k = spring constant b = damping constant Equations Of Motion

See also https://www.myphysicslab.com/collideSpring.html.

Spring force and damping look like this: text F = -k L -b v = -k (x - S1.getX() - R) - b v = m v' So equations of motion are: text x' = v v' = -(k/m)(x - S1.getX() - R) -(b/m) v Collision Handling

When colliding with a wall, just reverse the velocity.

When the two blocks collide, adjust the velocities of particles as follows:

Let vcm = velocity of center of mass of block 1 and 2.
Let v1 = velocity of block 1 before collision
Let v1_after = velocity of block 1 after collision

To find new velocity of block 1, find the velocity in the center of mass frame and reflect it. This works out to -v1 + 2 vcm. Here's the derivation:

Velocity of block 1 in cm frame is v1 - vcm.

In center of mass frame, total momentum is zero; after collision momentum is
preserved; so we just reverse signs of each velocity in cm frame.
Reflection of velocity is
```text
-(v1 - vcm) = vcm - v1

Add back vcm to get to laboratory frame:

v1_after = vcm + (vcm - v1) = 2 vcm - v1

Same derivation applies for block 2.

To Do

Elasticity parameter.

Hierarchy (view full)

Implements

Constructors

constructor

Properties

collisionFunction_ debugPaint_ initialState_

Methods

addCollision addObserver addParameter broadcast broadcastParameter evaluate findCollisions finishDrag getBroadcast getClassName getDamping getEnergyInfo getMass1 getMass2 getMomentum getName getObservers getPEOffset getParameter getParameterBoolean getParameterNumber getParameterString getParameters getSimList getSpring1Length getSpring1Stiffness getSpring2Length getSpring2Stiffness getTime getVarsList handleCollisions handleKeyEvent modifyObjects mouseDrag moveObjects removeObserver removeParameter reset restoreState saveInitialState saveState setBroadcast setCollisionFunction setDamping setDebugPaint setMass1 setMass2 setPEOffset setSpring1Length setSpring1Stiffness setSpring2Length setSpring2Stiffness setTerminal setVarsList startDrag toString toStringShort

Constructors

constructor

Properties

collisionFunction_

collisionFunction_: null | ((bc, t) => void) = null

Function to print collisions, or null to turn off printing collisions.

Type declaration

Private debugPaint_

debugPaint_: null | (() => void) = null

Function to paint canvases, for debugging. If defined, this will be called within moveObjects() so you can see the simulation state after each time step (you will need to arrange your debugger to pause after each invocation of debugPaint_ to see the state).

Type declaration

    • (): void

    • Returns void

Protected initialState_

initialState_: null | number[] = null

Initial values.

Methods

Private addCollision

addObserver

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.

findCollisions

  • findCollisions(collisions, vars, stepSize): void

  • Finds collisions based on the passed in state variables. Can rely on modifyObjects having been called prior, with this set of state variables. Uses the state saved by saveState as the 'before' state for comparison.

    The list of collisions that are passed in can potentially have collisions from the near future that were found previously. The CollisionSim should avoid adding collisions that are duplicates of those already on the list.

    Parameters

    • collisions: BlockCollision[]

      the list of collisions to add to

    • vars: number[]

      the current array of state variables

    • stepSize: number

      the size of the current time step, in seconds

    Returns void

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

getDamping

getEnergyInfo

getMass1

getMass2

getMomentum

getName

getObservers

getPEOffset

getParameter

getParameterBoolean

getParameterNumber

getParameterString

getParameters

getSimList

getSpring1Length

getSpring1Stiffness

getSpring2Length

getSpring2Stiffness

getTime

getVarsList

handleCollisions

  • handleCollisions(collisions, opt_totals?): boolean

  • Adjusts the simulation state based on the given Collisions. For example, this might reverse the velocities of objects colliding against a wall. The simulation state is contained in the vars array of state variables from getVarsList.

    Note that these Collisions will typically be from the very near future; CollisionAdvance backs up to just before the moment of collision before handling Collisions.

    Parameters

    • collisions: BlockCollision[]

      the list of current collisions

    • Optional opt_totals: CollisionTotals

      CollisionTotals object to update with number of collisions handled

    Returns boolean

    true if was able to handle the collision, changing state of simulation.

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

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

setCollisionFunction

  • setCollisionFunction(f): void

  • Sets a function for printing collisions. The function is called whenever a collision occurs. The function takes two variables: a BlockCollision and a Terminal. This can be defined from within the Terminal by the user. Here is an example usage

    sim.setCollisionFunction(function(c,t) {
      const s = c.getDetectedTime().toFixed(2)+"\t"
        +c.getImpulse().toFixed(2)+"\t"
        +c.rightBlock_.getPosition().getX().toFixed(2)+"\t"
        +c.leftBlock_.getName()+"\t"
        +c.rightBlock_.getName();
      t.println(s);
    })

    Parameters

    • f: null | ((bc, t) => void)

      the function to print collisions, or null to turn off printing collisions

    Returns void

setDamping

setDebugPaint

  • setDebugPaint(fn): void

  • For debugging, specify a function that will paint canvases, so that you can see the simulation while stepping thru with debugger.

    Parameters

    • fn: null | (() => void)

      function that will paint canvases

    Returns void

setMass1

setMass2

setPEOffset

setSpring1Length

setSpring1Stiffness

setSpring2Length

setSpring2Stiffness

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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