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(sec-item-nodegenericode2)=
# NodeGenericODE2

A node containing a number of {ref}`ODE2 <ODE2>` variables. Use this node e.g. for scalar dynamic equations (Mass1D), for ObjectGenericODE2 or for the Eulerian coordinate in the ALECable element. NOTE: referenceCoordinates and all initialCoordinates(_t) must be initialized, because no default values exist.

## Interface

- Provides: `GenericODE2`
- Objects that take this node: [](#sec-item-objectmass1d), [](#sec-item-objectrotationalmass1d), [](#sec-item-objectkinematictree)

## Parameters

The parameters of the item; in a dictionary, its type is 'GenericODE2':

| name | type | size | default | description |
|---|---|---|---|---|
| **name** | String |  | '' | node's unique name |
| **referenceCoordinates** | Vector |  | [] | (symbol: $\qv\cRef = [q_0,\,\ldots,\,q_{nc}]\tp\cRef$) generic reference coordinates of node; must be consistent with numberOfODE2Coordinates |
| **initialCoordinates** | Vector |  | [] | (symbol: $\qv\cIni = [q_0,\,\ldots,\,q_{nc}]\tp\cIni$) initial displacement coordinates; must be consistent with numberOfODE2Coordinates |
| **initialCoordinates_t** | Vector |  | [] | (symbol: $\dot \qv\cIni = [\dot q_0,\,\ldots,\,\dot q_{n_c}]\tp\cIni$) initial velocity coordinates; must be consistent with numberOfODE2Coordinates |
| **numberOfODE2Coordinates** | PInt |  | 0 | (symbol: $n_c$) number of generic {ref}`ODE2 <ODE2>` coordinates; **must be given**: the default is only a placeholder |
| **visualization** | VNodeGenericODE2 |  |  | parameters for visualization of item |

## Visualization parameters

`VNodeGenericODE2` has no parameters.

## Drawing

The item draws nothing.

## Output variables

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

```{tabularcolumns} \Y{0.25}\Y{0.25}\Y{0.5}
```

| output variable | symbol | description |
|---|---|---|
| CoordinatesTotal |  | displacement plus reference coordinates of node |
| Coordinates | $\qv\cConfig = [q_0,\,\ldots,\,q_{nc}]\tp\cConfig$ | coordinates vector of node |
| Coordinates_t | $\dot \qv\cConfig = [\dot q_0,\,\ldots,\,\dot q_{nc}]\tp\cConfig$ | velocity coordinates vector of node |
| Coordinates_tt | $\ddot \qv\cConfig = [\ddot q_0,\,\ldots,\,\ddot q_{nc}]\tp\cConfig$ | acceleration coordinates vector of node |

(description-nodegenericode2)=
## Detailed description

### Coordinates

A number of {ref}`ODE2 <ODE2>` coordinates, `numberOfODE2Coordinates`, whose meaning is **defined by the
object that uses the node**: the modal coordinates of `ObjectFFRFreducedOrder`, the joint
coordinates of `ObjectKinematicTree`, the coordinates of `ObjectGenericODE2`, or the axial motion of
`ObjectALEANCFCable2D`. The current value of a coordinate is its reference value plus its current
coordinate, $c_i = q_{i,\mathrm{ref}} + q_i$.

### Action on the equations of motion

Each coordinate leads to one {ref}`ODE2 <ODE2>` equation, which the object provides; the node itself adds
nothing.

(miniexample-nodegenericode2)=
## Mini example


```python
#two coordinates of a user-defined second-order system: a mass on a spring and a free mass
node = mbs.AddNode(NodeGenericODE2(numberOfODE2Coordinates=2, referenceCoordinates=[0,0],
                                   initialCoordinates=[0.1,0], initialCoordinates_t=[0,1]))
M = np.diag([1,1])
K = np.diag([(2*np.pi)**2, 0]) #eigenfrequency 1 Hz for the first coordinate
mbs.AddObject(ObjectGenericODE2(nodeNumbers=[node], massMatrix=M, stiffnessMatrix=K))

mbs.Assemble()
mbs.SolveDynamic()

#after one period, q0 = 0.1 again; q1 = 1*t
exu.sys['testResult'] = sum(mbs.GetNodeOutput(node, exu.OutputVariableType.Coordinates)) #1.1
```


Relevant Examples (Ex) and TestModels (TM) with weblink to github: [`ALEANCFpipe.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/Examples/ALEANCFpipe.py) (Ex), [`ANCFALEtest.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/Examples/ANCFALEtest.py) (Ex), [`ANCFmovingRigidbody.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/Examples/ANCFmovingRigidbody.py) (Ex), [`beltDriveALE.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/Examples/beltDriveALE.py) (Ex), [`craneReevingSystem.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/Examples/craneReevingSystem.py) (Ex), [`kinematicTreeAndMBS.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/Examples/kinematicTreeAndMBS.py) (Ex), [`nMassOscillator.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/Examples/nMassOscillator.py) (Ex), [`nMassOscillatorInteractive.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/Examples/nMassOscillatorInteractive.py) (Ex), [`reinforcementLearningRobot.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/Examples/reinforcementLearningRobot.py) (Ex), [`simulateInteractively.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/Examples/simulateInteractively.py) (Ex), [`stiffFlyballGovernorKT.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/Examples/stiffFlyballGovernorKT.py) (Ex), [`ANCFmovingRigidBodyTest.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/TestModels/ANCFmovingRigidBodyTest.py) (TM), [`ANCFslidingAndALEjointTest.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/TestModels/ANCFslidingAndALEjointTest.py) (TM), [`energiesFlexibleBodiesTest.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/TestModels/energiesFlexibleBodiesTest.py) (TM), [`energiesTest.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/TestModels/energiesTest.py) (TM), ...