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(sec-item-markerobjectode2coordinates)=
# MarkerObjectODE2Coordinates

A Marker attached to all coordinates of an object (currently only body is possible), e.g. to apply special constraints or loads on all coordinates. The measured coordinates INCLUDE reference + current coordinates.

## 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 'ObjectODE2Coordinates':

| name | type | size | default | description |
|---|---|---|---|---|
| **name** | String |  | '' | marker's unique name |
| **objectNumber** | ObjectIndex |  | invalid (-1) | body number to which marker is attached to |
| **visualization** | VMarkerObjectODE2Coordinates |  |  | parameters for visualization of item |

## Visualization parameters

`VMarkerObjectODE2Coordinates` has no parameters.

## Drawing

The item draws nothing.
(description-markerobjectode2coordinates)=
## Detailed description

### Marker quantities

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

### Jacobians

The unit matrix of the size of the body's coordinates. On a body without coordinates (ground) the
values and the Jacobian are empty.

(miniexample-markerobjectode2coordinates)=
## Mini example


```python
#all coordinates of an object, here of a ObjectGenericODE2 with two free coordinates, tied by a
#coordinate vector constraint X1 q - X0 q_ground = offset, which is q0 - q1 = 0
node = mbs.AddNode(NodeGenericODE2(numberOfODE2Coordinates=2, referenceCoordinates=[0,0],
                                   initialCoordinates=[0,0], initialCoordinates_t=[0,0]))
oGeneric = mbs.AddObject(ObjectGenericODE2(nodeNumbers=[node], massMatrix=np.eye(2)))
mAll = mbs.AddMarker(MarkerObjectODE2Coordinates(objectNumber=oGeneric))
mNone = mbs.AddMarker(MarkerNodeCoordinates(nodeNumber=nGround)) #the ground node has no coordinates
mbs.AddObject(ObjectConnectorCoordinateVector(markerNumbers=[mNone, mAll], scalingMarker0=np.zeros((1,0)),
                                             scalingMarker1=[[1,-1]], offset=[0]))
mbs.AddLoad(LoadCoordinate(markerNumber=mbs.AddMarker(MarkerNodeCoordinate(nodeNumber=node, coordinate=0)), load=2))

mbs.Assemble()
mbs.SolveDynamic()

#both coordinates move together: a = F/2 = 1, q1 = a/2*t^2 at t=1
exu.sys['testResult'] = mbs.GetNodeOutput(node, exu.OutputVariableType.Coordinates)[1] #0.5
```


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