# Class SpringNonLinear1

Represents a non-linear spring attached between two MassObjects, generates a Force which depends on how the SpringNonLinear1 is stretched. Damping is proportional to the relative velocity of the two objects.

The force equation is:

``````f(x) = S(6*Math.pow(x,-1) - Math.pow(x/2, -3))
x = distance between masses
S = resisting force constant
``````

The potential energy is the integral of the force:

``````PE(x) = S(6 * Math.log(x) + 4*Math.pow(x, -2))
``````

The minimum PE occurs where the force is zero:

``````S(6*Math.pow(x,-1) = Math.pow(x/2, -3))
6/x = 8 x^-3
3/4 = x^-2
x_min = sqrt(4/3) = 2/sqrt(3)
``````

We subtract the minimum PE from the reported PE so that PE is zero at it's minimum.

To attach one end to a fixed point you can attach to an infinite mass MassObject or a Scrim.

## Constructors

• #### Parameters

• ##### name: string

language-independent name of this object

• ##### body1: MassObject

body to attach to start point of the SpringNonLinear1

• ##### attach1_body: GenericVector

attachment point in body coords of body1

• ##### body2: MassObject

body to attach to end point of the SpringNonLinear1

• ##### attach2_body: GenericVector

attachment point in body coords of body2

• ##### restLength: number

length of spring when it has no force

• ##### `Optional`stiffness: number

amount of force per unit distance of stretch

## Properties

minPE_: number = 0

minimum potential energy

ID: number = 1

Counter used for naming SimObjects.

## Methods

• Returns attachment point for body 1, in body coordinates of body 1.

#### Returns Vector

attachment point for body 1, in body coordinates of body 1.

• Returns attachment point for body 2, in body coordinates of body 2.

#### Returns Vector

attachment point for body 2, in body coordinates of body 2.

• Returns the RigidBody that start point of the spring is attached to.

#### Returns MassObject

the RigidBody that start point of the spring is attached to.

• Returns the RigidBody that end point of the spring is attached to.

#### Returns MassObject

the RigidBody that end point of the spring is attached to.

• Returns the amount of damping for this spring. Damping is proportional to the relative velocity of the two points.

#### Returns number

amount of damping for this spring

• Returns the expiration time, when this SimObject should be removed from the SimList. This is intended for temporary SimObjects that illustrate, for example, contact forces or collisions.

#### Returns number

the expiration time, in time frame of the Simulation clock

• Returns the distance between start and end points of this spring

#### Returns number

the distance between start and end points of this spring

• Name of this SimObject, either the language-independent name for scripting purposes or the localized name for display to user.

The language-independent name should be the same as the English version but capitalized and with spaces and dashes replaced by underscore, see Util.toName, nameEquals.

The name should give an idea of the role of the SimObject in the simulation. This allows us to to treat an object in a special way depending on its name. For example, we might use the name to decide what type of DisplayObject to create to represent the SimObject.

#### Parameters

• ##### `Optional`opt_localized: boolean

`true` means return the localized version of the name; default is `false` which means return the language independent name.

#### Returns string

name of this SimObject

• Returns the length of this spring when no force is applied.

#### Returns number

rest length of this spring

• Positive stretch means the spring is expanded, negative stretch means compressed.

#### Returns number

the amount that this line is stretched from its rest length

• Returns length of spring that has minimum potential energy.

#### Returns number

length of spring that has minimum potential energy

• Whether this SimObject has the given name, adjusting for transformation to the language-independent form of the name, as is done by Util.toName.

#### Parameters

• ##### name: string

the English or language-independent version of the name

#### Returns boolean

whether this SimObject has the given name (adjusted to language-independent form)

• Returns potential energy for a given length of spring.

#### Parameters

• ##### len: number

length of spring

#### Returns number

potential energy

• Sets the value of damping for this spring. Damping is proportional to the relative velocity of the two points.

#### Parameters

• ##### damping: number

the value of damping for this spring

#### Returns Spring

this Spring to allow chaining of setters

• Sets the expiration time, when this SimObject should be removed from the SimList. This is intended for temporary SimObjects that illustrate, for example, contact forces or collisions.

#### Parameters

• ##### time: number

the expiration time, in time frame of the Simulation clock

#### Returns void

• Sets the rest length of this spring, which is used for calculating the stretch. When length of spring is the rest length, then no force is applied at either end.

#### Parameters

• ##### value: number

the rest length of this spring

#### Returns void

• Sets stiffness of this spring

#### Parameters

• ##### stiffness: number

the stiffness of this spring

#### Returns void

• Returns true if the given SimObject is similar to this SimObject for display purposes. SimObjects are similar when they are the same type and nearly the same size and location. Mainly used when showing forces - to avoid adding too many objects to the display. See SimList.getSimilar.

#### Parameters

• ##### obj: SimObject

the SimObject to compare to

• ##### `Optional`_opt_tolerance: number

the amount the object components can differ by

#### Returns boolean

true if this SimObject is similar to `obj` for display purposes

• 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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