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(sec-item-markernodecoordinates)=
# MarkerNodeCoordinates

A node-Marker attached to all {ref}`ODE2 <ODE2>` coordinates of a node. IN CONTRAST to MarkerNodeCoordinate, the marker coordinates INCLUDE the reference values! For {ref}`ODE1 <ODE1>` coordinates use `MarkerNodeODE1Coordinates`.

## Interface

- Provides: `Coordinates`
- Connectors, constraints and loads that can use it: [](#sec-item-objectconnectorcoordinatevector)

## Parameters

The parameters of the item; in a dictionary, its type is 'NodeCoordinates':

| name | type | size | default | description |
|---|---|---|---|---|
| **name** | String |  | '' | marker's unique name |
| **nodeNumber** | NodeIndex |  | invalid (-1) | node number to which marker is attached to |
| **visualization** | VMarkerNodeCoordinates |  |  | parameters for visualization of item |

## Visualization parameters

`VMarkerNodeCoordinates` has no parameters.

## Drawing

The item draws nothing.
(description-markernodecoordinates)=
## Detailed description

### Marker quantities

| quantity | symbol | as computed |
|---|---|---|
| coordinates | $\cv = \qv\cRef + \qv$ | **all** {ref}`ODE2 <ODE2>` coordinates of the node, **including** their reference values |
| their velocities | $\dot\cv = \dot\qv$ | the time derivatives |

Unlike `MarkerNodeCoordinate`, the values include the reference values.

### Jacobians

The unit matrix of the size of the node's coordinates: a vector of forces acts on the coordinates
one by one. On a node without {ref}`ODE2 <ODE2>` coordinates the values and the Jacobian are
empty.

(miniexample-markernodecoordinates)=
## Mini example


```python
#all coordinates of two nodes, tied by a coordinate vector constraint X1 qB - X0 qA = offset; the
#coordinates INCLUDE the reference values, so qB - qA = [1,0,0] keeps the two points where they are
nA = mbs.AddNode(NodePoint(referenceCoordinates=[0,0,0]))
nB = mbs.AddNode(NodePoint(referenceCoordinates=[1,0,0]))
mbs.AddObject(ObjectMassPoint(nodeNumber=nA, mass=1))
mbs.AddObject(ObjectMassPoint(nodeNumber=nB, mass=1))
mA = mbs.AddMarker(MarkerNodeCoordinates(nodeNumber=nA))
mB = mbs.AddMarker(MarkerNodeCoordinates(nodeNumber=nB))
mbs.AddObject(ObjectConnectorCoordinateVector(markerNumbers=[mA, mB], scalingMarker0=np.eye(3),
                                             scalingMarker1=np.eye(3), offset=[1,0,0]))
mbs.AddLoad(LoadForceVector(markerNumber=mbs.AddMarker(MarkerNodePosition(nodeNumber=nA)), loadVector=[2,0,0]))

mbs.Assemble()
mbs.SolveDynamic()

#both masses move together: a = F/(2m) = 1, x = a/2*t^2 at t=1
exu.sys['testResult'] = mbs.GetNodeOutput(nB, exu.OutputVariableType.Displacement)[0] #0.5
```


Relevant Examples (Ex) and TestModels (TM) with weblink to github: [`coordinateVectorConstraint.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/TestModels/coordinateVectorConstraint.py) (TM), [`coordinateVectorConstraintGenericODE2.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/TestModels/coordinateVectorConstraintGenericODE2.py) (TM), [`rigidBodyAsUserFunctionTest.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/TestModels/rigidBodyAsUserFunctionTest.py) (TM)