Class RigidDoublePendulumSim

Simulation of a double pendulum as two rigid bodies. This uses RigidBody's and Joint's, but only for geometry and display. This does not use the general physics engine ContactSim, instead this is a specialized simulation like DoublePendulumSim.

For derivation of equations of motion, see the paper Double Pendulum as Rigid Bodies by Erik Neumann, April 2, 2011.

TO DO: explain how and why the angle-1 variable is different from the angle-1 parameter. Perhaps rename the angle-1 parameter to be omega-1 to reduce confusion. Perhaps allow setting of the angle-1 variable directly, and then adapt accordingly.

TO DO: figure out what the real rest state is (it is not all zero angles), which will also fix the energy calculation.

TO DO: add damping

TO DO: derive equations of motion using Lagrangian method

Properties

L1_: number

distance from pivot 1 to pivot 2

R1_: number

distance from pivot 1 to the center of mass of pendulum 1

R2_: number

distance from pivot 2 to the center of mass of pendulum 2

gamma1_: number

Angle of R1 with respect to vertical in body coords of pendulum 1. Gamma adjustment angle is needed because vector R1 might not be vertical.

gamma2_: number

Angle of R2 with respect to vertical in body coords of pendulum 2.

gravity_: number = 9.8

gravity

initialState_: null | number[] = null

Initial values.

omega1_: number

initial angle of pendulum 1

omega2_: number

initial angle of pendulum 2

pendulum1_: RigidBody

upper pendulum

pendulum2_: RigidBody

lower pendulum

phi_: number

angle from vector r1 to vector l1

pivot1_: Joint

upper pivot, joins scrim and pendulum1

pivot2_: Joint

lower pivot, joins pendulum1 and pendulum2

potentialOffset_: number = 0

potential energy offset

Methods

• 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

• observer: Observer

the Observer to add

Returns void

• Adds the Parameter to the list of this Subject's available Parameters.

Parameters

• parameter: Parameter

the Parameter to add

Throws

if a Parameter with the same name already exists.

• Notifies all Observers that the Parameter with the given name has changed by calling observe on each Observer.

Parameters

• name: string

the language-independent or English name of the Parameter that has changed

Throws

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.

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.

• Returns angle of R1 with respect to vertical in body coords of pendulum 1.

Returns number

angle of R1 with respect to vertical in body coords of pendulum 1.

• Returns angle of R2 with respect to vertical in body coords of pendulum 2.

Returns number

angle of R2 with respect to vertical in body coords of pendulum 2.

• Removes the Observer from this Subject's list of Observers. An Observer may call `removeObserver` during its `observe` method.

Parameters

• observer: Observer

the Observer to detach from list of Observers

Returns void

• 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

• Sets the Terminal object that this simulation can print data into.

Parameters

• terminal: null | Terminal

the Terminal object that this simulation can print data into.

Returns void

• Sets the VarsList for this simulation.

Parameters

• varsList: VarsList

the VarsList to use in this simulation

Returns void

• 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.

• Returns angle between vertical (in body coordinates) and the vector from joint to center of mass of the pendulum. If the pendulum were hanging at rest from the joint with no forces other than gravity acting, then the angle of the pendulum would be `-gamma`.

Parameters

• pendulum: RigidBody

the pendulum RigidBody

• pivot: Joint

the Joint that the pendulum is hanging from

Returns number

angle between vertical (in body coordinates) and the vector from joint to center of mass of the pendulum

Throws

if the pendulum is not one of the bodies of the joint

• Creates a double pendulum with centered mass and joints. The two rectangular bodies are attached together as a double pendulum. The center of mass is at geometric center of each pendulum, and joints are along the vertical center line of each body.

Parameters

• theta1: number

angle at joint of scrim and pendulum1

• theta2: number

angle at joint of pendulum1 and pendulum2

• `Optional`pivot: Vector

location of fixed joint connecting to Scrim, in world coords

Returns Parts

• Creates a double pendulum with offset center of mass and offset joints. The two rectangular bodies are attached together as a double pendulum. The center of mass of the upper pendulum is offset from its geometric center. The joint connecting the two bodies is not along the vertical center line of either body, but is offset.

Parameters

• theta1: number

angle at joint of scrim and pendulum1

• theta2: number

angle at joint of pendulum1 and pendulum2

• `Optional`pivot: Vector

location of fixed joint connecting to Scrim, in world coords

Returns Parts

Generated using TypeDoc