WOLFRAM SYSTEMMODELER
WorldWorld coordinate system + gravity field + default animation definition 
SystemModel["Modelica.Mechanics.MultiBody.World"]
This information is part of the Modelica Standard Library maintained by the Modelica Association.
Model World represents a global coordinate system fixed in ground. This model serves several purposes:
Since the gravity field function is required from all bodies with mass and the default settings of animation properties are required from nearly every component, exactly one instance of model World needs to be present in every model on the top level. The basic declaration needs to be:
inner Modelica.Mechanics.MultiBody.World world
Note, it must be an inner declaration with instance name world in order that this world object can be accessed from all objects in the model. When dragging the "World" object from the package browser into the diagram layer, this declaration is automatically generated (this is defined via annotations in model World).
All vectors and tensors of a mechanical system are resolved in a frame that is local to the corresponding component. Usually, if all relative joint coordinates vanish, the local frames of all components are parallel to each other, as well as to the world frame (this holds as long as a Parts.FixedRotation, component is not used). In this "reference configuration" it is therefore alternatively possible to resolve all vectors in the world frame, since all frames are parallel to each other. This is often very convenient. In order to give some visual support in such a situation, in the icon of a World instance two axes of the world frame are shown and the labels of these axes can be set via parameters.
frame_b 
Type: Frame_b Description: Coordinate system fixed in the origin of the world frame 

enableAnimation 
Value: true Type: Boolean Description: = true, if animation of all components is enabled 

animateWorld 
Value: true Type: Boolean Description: = true, if world coordinate system shall be visualized 
animateGravity 
Value: true Type: Boolean Description: = true, if gravity field shall be visualized (acceleration vector or field center) 
label1 
Value: "x" Type: AxisLabel Description: Label of horizontal axis in icon 
label2 
Value: "y" Type: AxisLabel Description: Label of vertical axis in icon 
gravityType 
Value: GravityTypes.UniformGravity Type: GravityTypes Description: Type of gravity field 
g 
Value: 9.81 Type: Acceleration (m/s²) Description: Constant gravity acceleration 
n 
Value: {0, 1, 0} Type: Axis () Description: Direction of gravity resolved in world frame (gravity = g*n/length(n)) 
mue 
Value: 3.986e14 Type: Real (m³/s²) Description: Gravity field constant (default = field constant of earth) 
driveTrainMechanics3D 
Value: true Type: Boolean Description: = true, if 3dim. mechanical effects of Parts.Mounting1D/Rotor1D/BevelGear1D shall be taken into account 
axisLength 
Value: nominalLength / 2 Type: Distance (m) Description: Length of world axes arrows 
axisDiameter 
Value: axisLength / defaultFrameDiameterFraction Type: Distance (m) Description: Diameter of world axes arrows 
axisShowLabels 
Value: true Type: Boolean Description: = true, if labels shall be shown 
gravityArrowTail 
Value: {0, 0, 0} Type: Position[3] (m) Description: Position vector from origin of world frame to arrow tail, resolved in world frame 
gravityArrowLength 
Value: axisLength / 2 Type: Length (m) Description: Length of gravity arrow 
gravityArrowDiameter 
Value: gravityArrowLength / defaultWidthFraction Type: Diameter (m) Description: Diameter of gravity arrow 
gravitySphereDiameter 
Value: 12742000 Type: Diameter (m) Description: Diameter of sphere representing gravity center (default = mean diameter of earth) 
nominalLength 
Value: 1 Type: Length (m) Description: "Nominal" length of multibody system 
defaultAxisLength 
Value: nominalLength / 5 Type: Length (m) Description: Default for length of a frame axis (but not world frame) 
defaultJointLength 
Value: nominalLength / 10 Type: Length (m) Description: Default for the fixed length of a shape representing a joint 
defaultJointWidth 
Value: nominalLength / 20 Type: Length (m) Description: Default for the fixed width of a shape representing a joint 
defaultForceLength 
Value: nominalLength / 10 Type: Length (m) Description: Default for the fixed length of a shape representing a force (e.g., damper) 
defaultForceWidth 
Value: nominalLength / 20 Type: Length (m) Description: Default for the fixed width of a shape representing a force (e.g., spring, bushing) 
defaultBodyDiameter 
Value: nominalLength / 9 Type: Length (m) Description: Default for diameter of sphere representing the center of mass of a body 
defaultWidthFraction 
Value: 20 Type: Real Description: Default for shape width as a fraction of shape length (e.g., for Parts.FixedTranslation) 
defaultArrowDiameter 
Value: nominalLength / 40 Type: Length (m) Description: Default for arrow diameter (e.g., of forces, torques, sensors) 
defaultFrameDiameterFraction 
Value: 40 Type: Real Description: Default for arrow diameter of a coordinate system as a fraction of axis length 
defaultSpecularCoefficient 
Value: 0.7 Type: Real Description: Default reflection of ambient light (= 0: light is completely absorbed) 
defaultN_to_m 
Value: 1000 Type: Real (N/m) Description: Default scaling of force arrows (length = force/defaultN_to_m) 
defaultNm_to_m 
Value: 1000 Type: Real (N·m/m) Description: Default scaling of torque arrows (length = torque/defaultNm_to_m) 
ndim 
Value: if enableAnimation and animateWorld then 1 else 0 Type: Integer Description: 
ndim2 
Value: if enableAnimation and animateWorld and axisShowLabels then 1 else 0 Type: Integer Description: 
headLength 
Value: min(axisLength, axisDiameter * Types.Defaults.FrameHeadLengthFraction) Type: Length (m) Description: 
headWidth 
Value: axisDiameter * Types.Defaults.FrameHeadWidthFraction Type: Length (m) Description: 
lineLength 
Value: max(0, axisLength  headLength) Type: Length (m) Description: 
lineWidth 
Value: axisDiameter Type: Length (m) Description: 
scaledLabel 
Value: Modelica.Mechanics.MultiBody.Types.Defaults.FrameLabelHeightFraction * axisDiameter Type: Length (m) Description: 
labelStart 
Value: 1.05 * axisLength Type: Length (m) Description: 
gravityHeadLength 
Value: min(gravityArrowLength, gravityArrowDiameter * Types.Defaults.ArrowHeadLengthFraction) Type: Length (m) Description: 
gravityHeadWidth 
Value: gravityArrowDiameter * Types.Defaults.ArrowHeadWidthFraction Type: Length (m) Description: 
gravityLineLength 
Value: max(0, gravityArrowLength  gravityHeadLength) Type: Length (m) Description: 
ndim_pointGravity 
Value: if enableAnimation and animateGravity and gravityType == GravityTypes.UniformGravity then 1 else 0 Type: Integer Description: 
x_arrowLine 
Type: Shape Description: 


x_arrowHead 
Type: Shape Description: 

x_label 
Type: Lines Description: 

y_arrowLine 
Type: Shape Description: 

y_arrowHead 
Type: Shape Description: 

y_label 
Type: Lines Description: 

z_arrowLine 
Type: Shape Description: 

z_arrowHead 
Type: Shape Description: 

z_label 
Type: Lines Description: 

gravityArrowLine 
Type: Shape Description: 

gravityArrowHead 
Type: Shape Description: 

gravitySphere 
Type: Shape Description: 
Simple double pendulum with two revolute joints and two bodies 

Demonstrate how to initialize a double pendulum so that its tip starts at a predefined position 

Demonstrate usage of ForceAndTorque element 

Free flying body attached by two springs to environment 

Determine spring constant such that system is in steady state at given position 

Demonstrate line force with two point masses using a JointUPS and alternatively a LineForceWithTwoMasses component 

Simple pendulum with one revolute joint and one body 

Simple spring/damper/mass system 

Two point masses in a point gravity field 

Two point masses in a point gravity field (rotation of bodies is neglected) 

Rigidly connected point masses in a point gravity field 

Simple spring/damper/mass system 

Mass attached with a spring to the world frame 

Point mass hanging on a spring 

3dim. springs in series and parallel connection 

Single wheel rolling on ground starting from an initial speed 

Rolling wheel set that is driven by torques driving the wheels 

Rolling wheel set that is pulled by a force 

Demonstrate the modeling of heat losses 

Demonstrate the modeling of a userdefined gravity field 

Demonstrate the visualization of a sine surface, as well as a torus and a wheel constructed from a surface 

Model of one cylinder engine 

Model of one cylinder engine with gas force and preparation for assembly joint JointRRP 

Model of one cylinder engine with gas force and analytic loop handling 

V6 engine with 6 cylinders, 6 planar loops and 1 degreeoffreedom 

V6 engine with 6 cylinders, 6 planar loops, 1 degreeoffreedom and analytic handling of kinematic loops 

One kinematic loop with four bars (with only revolute joints; 5 nonlinear equations) 

One kinematic loop with four bars (with UniversalSpherical joint; 1 nonlinear equation) 

One kinematic loop with four bars (with JointSSP joint; analytic solution of nonlinear algebraic loop) 

Mechanism with three planar kinematic loops and one degreeoffreedom with analytic loop handling (with JointRRR joints) 

Model of one cylinder engine with gas force 

Demonstrates that a cylindrical body can be replaced by Rotor1D model 

Demonstrates usage of models Rotor1D and Mounting1D 

Demonstrates usage of model Rotor1D mounted on a moving body 

Demonstrate usage of GearConstraint model 

Demonstrates the usage of a BevelGear1D model and how to calculate the power of such an element 

Body attached by one spring and two prismatic joints or constrained to environment 

Body attached by one spring and revolute joint or constrained to environment 

Body attached by one spring and spherical joint or constrained to environment 

Body attached by one spring and universal joint or constrained to environment 

Visualizing an arrow with variable size; all data have to be set as modifiers (see info layer) 

Visualizing a double arrow with variable size; all data have to be set as modifiers (see info layer) 
Point mass used at all places of this example 

Body used at all places of the comparison model with zero inertia tensor 

Model of the mechanical part of the r3 robot (without animation) 

External force acting at frame_b, defined by 3 input signals and resolved in frame world, frame_b or frame_resolve 

External torque acting at frame_b, defined by 3 input signals and resolved in frame world, frame_b or frame_resolve 

External force and torque acting at frame_b, defined by 3+3 input signals and resolved in frame world, frame_b or in frame_resolve 

Force acting between two frames, defined by 3 input signals and resolved in frame world, frame_a, frame_b or frame_resolve 

Torque acting between two frames, defined by 3 input signals and resolved in frame world, frame_a, frame_b or frame_resolve 

Force and torque acting between two frames, defined by 3+3 input signals and resolved in frame world, frame_a, frame_b or frame_resolve 

General line force component with an optional point mass on the connection line 

General line force component with two optional point masses on the connection line 

Linear translational spring with optional mass 

Linear (velocity dependent) damper 

Linear spring and linear damper in parallel 

Linear spring and linear damper in series connection 

Force acting between two frames, defined by 3 input signals 

Torque acting between two frames, defined by 3 input signals 

External force acting at frame_b, defined by 3 input signals 

External torque acting at frame_b, defined by 3 input signals 

Base model for components providing two frame connectors + outer world + assert to guarantee that the component is connected 

Base model for components providing two frame connectors + outer world + assert to guarantee that the component is connected (default icon size is factor 2 larger as usual) 

Base model for components providing one frame_a connector + outer world + assert to guarantee that the component is connected 

Base model for components providing one frame_b connector + outer world + assert to guarantee that the component is connected 

Base model for elementary joints (has two frames + outer world + assert to guarantee that the joint is connected) 

Base model for force elements (provide frame_b.f and frame_b.t in subclasses) 

Base model for line force elements 

Base model to measure an absolute frame variable 

Base model to measure a relative variable between two frames 

Base model for visualizers (has a frame_a on the left side + outer world + assert to guarantee that the component is connected) 

Prismatic joint (1 translational degreeoffreedom, 2 potential states, optional axis flange) 

Revolute joint (1 rotational degreeoffreedom, 2 potential states, optional axis flange) 

Revolute joint that is described by 2 positional constraints for usage in a planar loop (the ambiguous cutforce perpendicular to the loop and the ambiguous cuttorques are set arbitrarily to zero) 

Cylindrical joint (2 degreesoffreedom, 4 potential states) 

Universal joint (2 degreesoffreedom, 4 potential states) 

Planar joint (3 degreesoffreedom, 6 potential states) 

Spherical joint (3 constraints and no potential states, or 3 degreesoffreedom and 3 states) 

Free motion joint (6 degreesoffreedom, 12 potential states) 

Free motion joint with scalar initialization and state selection (6 degreesoffreedom, 12 potential states) 

Spherical  spherical joint aggregation (1 constraint, no potential states) with an optional point mass in the middle 

Universal  spherical joint aggregation (1 constraint, no potential states) 

Ideal 3dim. gearbox (arbitrary shaft directions) 

Universal  prismatic  spherical joint aggregation (no constraints, no potential states) 

Universal  spherical  revolute joint aggregation (no constraints, no potential states) 

Universal  spherical  prismatic joint aggregation (no constraints, no potential states) 

Spherical  spherical  revolute joint aggregation with mass (no constraints, no potential states) 

Spherical  spherical  prismatic joint aggregation with mass (no constraints, no potential states) 

Planar revolute  revolute  revolute joint aggregation (no constraints, no potential states) 

Planar revolute  revolute  prismatic joint aggregation (no constraints, no potential states) 

Prismatic cutjoint and translational directions may be constrained or released 

Revolute cutjoint and translational directions may be constrained or released 

Spherical cut joint and translational directions may be constrained or released 

Universal cutjoint and translational directions may be constrained or released 

Revolute joint where the rotation angle is computed from a length constraint (1 degreeoffreedom, no potential state) 

Prismatic joint where the translational distance is computed from a length constraint (1 degreeoffreedom, no potential state) 

Frame fixed in the world frame at a given position 

Fixed translation of frame_b with respect to frame_a 

Fixed translation followed by a fixed rotation of frame_b with respect to frame_a 

Rigid body with mass, inertia tensor and one frame connector (12 potential states) 

Rigid body with mass, inertia tensor, different shapes for animation, and two frame connectors (12 potential states) 

Rigid body with box shape. Mass and animation properties are computed from box data and density (12 potential states) 

Rigid body with cylinder shape. Mass and animation properties are computed from cylinder data and density (12 potential states) 

Rigid body where body rotation and inertia tensor is neglected (6 potential states) 

Propagate 1dim. support torque to 3dim. system (provided world.driveTrainMechanics3D=true) 

1D inertia attachable on 3dim. bodies (3D dynamic effects are taken into account if world.driveTrainMechanics3D=true) 

1D inertia attachable on 3dim. bodies (3D dynamic effects are taken into account) 

1D gearbox with arbitrary shaft directions and 3dim. bearing frame (3D dynamic effects are taken into account provided world.driveTrainMechanics3D=true) 

Measure absolute kinematic quantities of frame connector 

Measure relative kinematic quantities between two frame connectors 

Measure the distance between the origins of two frame connectors 

Measure cut force vector 

Measure cut torque vector 

Measure cut force and cut torque vector 

Measure power flowing from frame_a to frame_b 

Base model to measure the cut force and/or torque between two frames, defined by components 

Base model to measure the cut force and/or torque between two frames, defined by equations (frame_resolve must be connected exactly once) 

Measure cut force vector (frame_resolve must be connected) 

Measure cut torque vector (frame_resolve must be connected) 

Visualizing an elementary shape with dynamically varying shape attributes (has one frame connector) 

Visualizing an elementary shape with dynamically varying shape attributes (has two frame connectors) 

Visualizing a coordinate system including axes labels (visualization data may vary dynamically) 

Visualizing an arrow with dynamically varying size in frame_a 

Visualizing an arrow with dynamically varying size in frame_a based on input signal 

Visualizing a torus 

Visualizing a voluminous wheel 

Visualizing a pipe with scalar field quantities along the pipe axis 

Visualizing a set of lines as cylinders (e.g., used to display characters) 