General info for all nodes

What a node is

A node provides coordinates and nothing else: no mass, no stiffness, no equations. The object that uses the node - a mass point, a rigid body, a finite element - provides the equations for its coordinates, and a node that no object uses leaves the system without equations for them. Each node page says, under Action on the equations of motion, which equations its coordinates get.

Reference, initial and current coordinates

Every node has referenceCoordinates, which define the reference configuration, and initialCoordinates and initialVelocities, which are relative to them: a NodePoint starts at referenceCoordinates + initialCoordinates. The coordinates of the system are the current coordinates, without the reference values - displacements, or changes of rotation parameters; the output variable Coordinates returns them and CoordinatesTotal adds the reference values. See Reference coordinates and displacements and Reference and current coordinates.

The kinds of coordinates

kind	what the solver does with it	nodes
ODE2	second order differential equations: positions, rotations, slopes	the point, rigid body and slope nodes, `Node1D`, `NodeGenericODE2`
ODE1	first order differential equations: states	`NodeGenericODE1`
AE	algebraic variables	`NodeGenericAE`; `NodeRigidBodyEP` adds one for its constraint
data	no unknowns: states an object updates between steps, such as contact or friction	`NodeGenericData`

NodePointGround has no coordinates at all.

Frames

The coordinates of a node are global, unless the object that uses the node reads them otherwise: ObjectFFRF reads the points of its mesh in the frame of its rigid body node. Every node page says under Frame and interpretation which objects deviate.

Rotation parametrizations

A rigid body is a rigid body node and an ObjectRigidBody, and the node decides how the rotation is parametrized; CreateRigidBody(..., nodeType=...) chooses it.

node	rotation coordinates	constraint	singularity	suited for
`NodeRigidBodyEP`	4 Euler parameters	one, \(\ttheta\tp\ttheta = 1\), added by the node	none	general 3D motion, implicit integration
`NodeRigidBodyRxyz`	3 Tait-Bryan angles	none	at \(\theta_1 = \pm\pi/2\)	small or planar-like rotations, readable angles
`NodeRigidBodyRotVecLG`	rotation vector	none	none in the Lie group update	arbitrary rotations, explicit and implicit Lie group integration
`NodeRigidBody2D`	1 angle about \(z\)	none	none	planar motion

In all of them, the torque equations are the torques projected with the transposed velocity transformation \(\Gm\tp\) of the node, \(\tomega = \Gm \dot\ttheta\).

Markers on nodes

A node marker needs the node to provide what it measures: MarkerNodePosition a position, MarkerNodeRigid a position and an orientation, MarkerNodeRotationCoordinate an orientation. The Interface of each node lists the markers and the objects that fit. MarkerNodeCoordinate and MarkerNodeCoordinates act on single coordinates and fit every node with ODE2 coordinates.

Drawing

A node is drawn if nodes.show and its own show are True: as a sphere of diameter nodes.defaultSize with nodes.tiling segments, or as a point with nodes.drawNodesAsPoint, in nodes.defaultColor or its own color; a size of -1 takes a fraction of openGL.advanced.initialMaxSceneSize. In a contour plot (contour.outputVariable, contour.outputVariableComponent) with contour.nodesColored, it takes the color of its value. nodes.showNumbers writes its number. A node without a position - Node1D, the generic nodes - draws nothing.

The settings: nodes.show, nodes.defaultSize, nodes.defaultColor, nodes.drawNodesAsPoint, nodes.tiling, nodes.showNumbers, contour.outputVariable, contour.outputVariableComponent, contour.nodesColored, openGL.advanced.initialMaxSceneSize.