Optional opt_name: stringname of this as a Subject
Function to print collisions, or null to turn off printing collisions.
Private debugFunction 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).
Private elasticity_bounciness of ball when colliding with track
Protected initialInitial values.
Private lowestlowest possible y coordinate of path
Private potentialpotential energy offset
Private stickiness_stickiness of track, determines when ball jumps from free flight onto track
Private xrange of x values of the path
Private xrange of x values of the path
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.
the Observer to add
Adds the Parameter to the list of this Subject's available Parameters.
the Parameter to add
if a Parameter with the same name already exists.
Notifies all Observers that this Subject has changed by calling observe on each Observer.
An Observer may call addObserver or removeObserver during its observe
method.
a SubjectEvent with information relating to the change
Notifies all Observers that the Parameter with the given name has changed by calling observe on each Observer.
the language-independent or English name of the Parameter that has changed
if there is no Parameter with the given name
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.
the current array of state variables (input),
corresponding to the state at getTime() + timeStep
array of change rates for each variable (output), all values are zero on entry.
the current time step (might be zero)
null if the evaluation succeeds, otherwise an object relating to the
error that occurred. The change array contains the output results.
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.
the list of collisions to add to
the current array of state variables
the size of the current time step, in seconds
Called at the end of a mouse drag operation, performs whatever action is
appropriate. Only called if startDrag returned true.
the SimObject being dragged, or null if no SimObject was found
the location of the mouse in
simulation coordinates of the SimView where simObject was found, or in the
focus view
if simObject is null.
distance from the initial object position to the mouse location at start of drag.
Protected getReturns whether broadcasting is enabled for this Subject. See setBroadcast.
whether broadcasting is enabled for this Subject
Returns the current EnergyInfo for this system.
an EnergyInfo object representing the current energy of this system.
Returns the ParameterBoolean with the given name.
the language-independent or English name of the ParameterBoolean
the ParameterBoolean with the given name
if there is no ParameterBoolean with the given name
Returns the ParameterNumber with the given name.
the language-independent or English name of the ParameterNumber
the ParameterNumber with the given name
if there is no ParameterNumber with the given name
Returns the ParameterString with the given name.
the language-independent or English name of the ParameterString
the ParameterString with the given name
if there is no ParameterString with the given name
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.
the list of current collisions
Optional opt_totals: CollisionTotalsCollisionTotals object to update with number of collisions handled
true if was able to handle the collision, changing state of simulation.
Called when a key is pressed or released, performs whatever action is appropriate for that event.
the KeyboardEvent that happened
true means this is a key-down event; false means a key-up event
the modifier keys down during event
Private jumpPossibly switch mode from track to free-flying.
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.
the SimObject being dragged, or null if no SimObject was found
the location of the mouse in
simulation coordinates of the SimView where simObject was found, or in the
focus view
if simObject is null.
distance from the initial object position (from DisplayObject.getPosition) to the mouse location at start of drag.
Private movePrivate off_Private off_Removes the Observer from this Subject's list of Observers. An Observer may
call removeObserver during its observe method.
the Observer to detach from list of Observers
Removes the Parameter from the list of this Subject's available Parameters.
the Parameter to remove
Sets the Simulation back to its initial conditions, see saveInitialState, and calls modifyObjects. Broadcasts event named 'RESET'.
Restores the Simulation state that was saved with saveState.
Saves the current variables and time as the initial state, so that this initial state can be restored with reset. Broadcasts event named 'INITIAL_STATE_SAVED'.
Saves the current state of the Simulation, so that we can back up to this state later on. The state is defined mainly by the set of Simulation variables, see getVarsList, but can include other data. This state is typically used for collision detection as the before collision state, see CollisionSim.findCollisions.
Protected setSets 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.
whether this Subject should broadcast events
the previous value
Sets a function for printing collisions. The function is called whenever a collision occurs. The function takes two variables: a RollerCollision 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.getPathPoint().getX().toFixed(2)+"\t"
+c.getPathPoint().getY().toFixed(2);
t.println(s);
})
the function to print collisions, or null to turn off printing collisions
Sets the Terminal object that this simulation can print data into.
the Terminal object that this simulation can print data into.
Protected setSets the VarsList for this simulation.
the VarsList to use in this simulation
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.
the SimObject that is nearest to the mouse drag coordinates,
or null if no SimObject was found
the location of the mouse in
simulation coordinates of the SimView where simObject was found, or in the
focus view
if simObject is null.
distance from the initial object position (from DisplayObject.getPosition) to the mouse location at start of drag
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
the modifier keys down during event
true if the EventHandler will handle dragging the SimObject
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'}}
a minimal string representation of this object.
Generated using TypeDoc
Simulation of a ball moving on a track, where the ball can fly off the track.
See https://www.myphysicslab.com/RollerFlight.html for additional explanations of the math involved here.
Radial Acceleration
This version of the roller coaster simulation has the ball jump off the track when appropriate.
The acceleration for uniform circular motion is
a = v^2/r.Suppose the ball is going over a hill. The minimum radial acceleration to keep the ball on the track is
v^2/r, wherer =radius of curvature of the track (at the point where the ball currently is).The actual acceleration normal to the track is given by the component of gravity (and other forces, eg. spring) that are normal to the track. If the actual acceleration is less than the minimum acceleration then the ball leaves the track.
Radius of Curvature
The radius of curvature of the track is given by reciprocal of
kappaAnother way to get it is:
On Track vs. Off Track
There is a different set of variables and equations depending on whether the ball is on or off the track. We keep a 'track/free mode' flag in the VarsList:
That Variable broadcasts itself whenever it changes.
On the track, the equations are similar to those of RollerDoubleSim; we have 2 variables:
When the ball leaves the track, the equations are similar to those of Spring2DSim; we have 4 variables:
Storing track or free mode in
vars[6]is useful for backing up in time; it allows thevarsto hold the complete state.Equations of Motion
See RollerDoubleSim and Spring2DSim for derivations.
On the track:
Off the track:
Without a spring force, the off-the-track equations of motion are:
Collisions
To detect collisions: see if the ball is below the track. We require that the track has no loops, so each x has a single point of the track above or below it. To handle the collision, we reflect the velocity in the tangent of the curve.
Math in
handleCollisionsFrom vector algebra:
TO DO Add to docs the mathematica file 'roller.nb' where curves like Hump and others were worked out.
TO DO To have a track with loops and vertical lines we need to have a way to determine what is inside or outside, or which direction the track inhibits movement. Need to deal with track sections that are vertical lines (infinite slope) & straight lines (infinite radius).