NodePoint2D

A 2D point node for point masses or solid finite elements which has 2 displacement degrees of freedom for ODE2.

Interface

Python names: NodePoint2D or Point2D, and VPoint2D for its visualization
Provides: Position2D
Node markers that can be attached: MarkerNodePosition
Objects that take this node: ObjectMassPoint2D

Parameters

The parameters of the item; in a dictionary, its type is ‘Point2D’:

name	type	size	default	description
name	String		‘’	node’s unique name
referenceCoordinates	Vector2D	2	[0.,0.]	(symbol: \(\qv\cRef = [q_0,\,q_1]\tp\cRef = \pv\cRef = [r_0,\,r_1]\tp\)) reference coordinates of node ==> e.g. ref. coordinates for finite elements; global position of node without displacement
initialCoordinates	Vector2D	2	[0.,0.]	(symbol: \(\qv\cIni = [q_0,\,q_1]\cIni\tp = [u_0,\,u_1]\cIni\tp\)) initial displacement coordinate
initialVelocities	Vector2D	2	[0.,0.]	(symbol: \(\dot\qv\cIni = \vv\cIni = [\dot q_0,\,\dot q_1]\cIni\tp\)) initial velocity coordinate
visualization	VNodePoint2D			parameters for visualization of item

Visualization parameters

The parameters of VNodePoint2D, given as visualization:

name	type	size	default	description
show	Bool		True	set true, if item is shown in visualization and false if it is not shown
drawSize	float		-1.	drawing size (diameter, dimensions of underlying cube, etc.) for item; size == -1.f means that default size is used
color	Float4	4	[-1.,-1.,-1.,-1.]	Default RGBA color for nodes; 4th value is alpha-transparency; R=-1.f means, that default color is used

Drawing

Drawn as all nodes.

Output variables

Available as OutputVariableType in sensors, Get...Output() and other functions:

output variable	symbol	description
Position	\(\pv\cConfig = [p_0,\,p_1,\,0]\cConfig\tp= \uv\cConfig + \pv\cRef\)	global 3D position vector of node; \(\uv\cRef=0\)
Displacement	\(\uv\cConfig = [q_0,\,q_1,\,0]\cConfig\tp\)	global 3D displacement vector of node
Velocity	\(\vv\cConfig = [\dot q_0,\,\dot q_1,\,0]\cConfig\tp\)	global 3D velocity vector of node
Acceleration	\(\av\cConfig = [\ddot q_0,\,\ddot q_1,\,0]\cConfig\tp\)	global 3D acceleration vector of node
CoordinatesTotal	\(\cv\cConfig = \uv\cConfig + \pv\cRef\)	displacement plus reference coordinates of node
Coordinates	\(\cv\cConfig = [q_0,\,q_1]\tp\cConfig\)	coordinate vector of node
Coordinates_t	\(\dot\cv\cConfig = [\dot q_0,\,\dot q_1]\tp\cConfig\)	velocity coordinates vector of node
Coordinates_tt	\(\ddot\cv\cConfig = \av\cConfig = [\ddot q_0,\,\ddot q_1]\tp\cConfig\)	acceleration coordinates vector of node
RotationMatrix		identity matrix (only for completeness)
Rotation	\([0,0,0]\)	(only for completeness)
AngularVelocity	\([0,0,0]\)	(only for completeness)
AngularVelocityLocal	\([0,0,0]\)	(only for completeness)

Detailed description

Coordinates

index	symbol	kind	meaning	frame
0, 1	\(q_0,\,q_1\)	ODE2	displacement of the node in \(x\) and \(y\)	global

Configuration

In any configuration, the position of the node is its reference position plus its displacement, with a third component that is always zero,

\[ \pv\cConfig = \vr{r_{0}}{r_{1}}{0}\cRef + \vr{q_0}{q_1}{0}\cConfig . \]

Frame and interpretation

The coordinates are displacements in the global \(x\)-\(y\) plane; ObjectMassPoint2D is the object that uses them.

Action on the equations of motion

The two coordinates lead to two ODE2 equations, the residuals of the forces in \(x\) and \(y\); a force of a load or connector enters them with its first two components.

Example: see ObjectMassPoint2D

Mini example

#a planar point mass under gravity, thrown with an initial velocity
node = mbs.AddNode(NodePoint2D(referenceCoordinates=[0,0], initialVelocities=[1,2]))
oMass = mbs.AddObject(ObjectMassPoint2D(nodeNumber=node, mass=1))
mMass = mbs.AddMarker(MarkerNodePosition(nodeNumber=node))
mbs.AddLoad(LoadForceVector(markerNumber=mMass, loadVector=[0,-9.81,0]))

mbs.Assemble()
mbs.SolveDynamic()

#y = v0*t - g/2*t^2 at t=1
exu.sys['testResult'] = mbs.GetNodeOutput(node, exu.OutputVariableType.Position)[1] #2-4.905=-2.905

Examples (Ex) and TestModels (TM) that show this item, with weblink to github: pendulum2Dconstraint.py (Ex), SliderCrank.py (Ex), SpringDamperMassUserFunction.py (Ex), slidercrankWithMassSpring.py (Ex)