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(sec-item-objectgenericode1)=
# ObjectGenericODE1

A system of $n$ {ref}`ODE1 <ODE1>`, having a system matrix, a rhs vector, but mostly it will use a user function to describe special {ref}`ODE1 <ODE1>` systems. It is based on NodeGenericODE1 nodes. NOTE that all matrices, vectors, etc. must have the same dimensions $n$ or $(n \times n)$, or they must be empty $(0 \times 0)$, using [] in Python.

## Interface

- Nodes: see the detailed description

## Parameters

The parameters of the item; in a dictionary, its type is 'GenericODE1':

| name | type | size | default | description |
|---|---|---|---|---|
| **name** | String |  | '' | objects's unique name |
| **nodeNumbers** | ArrayNodeIndex |  | [] | (symbol: $\mathbf{n}_n = [n_0,\,\ldots,\,n_n]\tp$) node numbers which provide the coordinates for the object (consecutively as provided in this list) |
| **systemMatrix** | NumpyMatrix |  | [] | (symbol: $\Am \in \Rcal^{n \times n}$) system matrix (state space matrix) of first order ODE |
| **rhsVector** | NumpyVector |  | [] | (symbol: $\fv \in \Rcal^{n}$) a constant rhs vector (e.g., for constant input) |
| **rhsUserFunction** | ObjectGenericODE1RhsUserFunction |  | 0 | (symbol: $\fv_{user} \in \Rcal^{n}$) A Python user function which computes the right-hand-side (rhs) of the first order ODE; see description below |
| **coordinateIndexPerNode** | ArrayIndex |  | [] | this list contains the local coordinate index for every node, which is needed, e.g., for markers; the list is generated automatically every time parameters have been changed |
| **tempCoordinates** | NumpyVector |  | [] | (symbol: $\cv_{temp} \in \Rcal^{n}$) temporary vector containing coordinates |
| **tempCoordinates_t** | NumpyVector |  | [] | (symbol: $\dot \cv_{temp} \in \Rcal^{n}$) temporary vector containing velocity coordinates |
| **visualization** | VObjectGenericODE1 |  |  | parameters for visualization of item |

## Visualization parameters

`VObjectGenericODE1` 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 |  | all {ref}`ODE2 <ODE2>` displacement plus reference coordinates of object |
| Coordinates |  | all {ref}`ODE1 <ODE1>` coordinates |
| Coordinates_t |  | all {ref}`ODE1 <ODE1>` velocity coordinates |

(description-objectgenericode1)=
## Detailed description

### Coordinates

An object with node numbers $[n_0,\,\ldots,\,n_n]$ and according numbers of nodal coordinates $[n_{c_0},\,\ldots,\,n_{c_n}]$, the total number of equations (=coordinates) of the object is

$$
n = \sum_{i} n_{c_i},
$$

which is used throughout the description of this object.

### Equations of motion

$$
\dot \qv = \fv + \fv_{user}(mbs, t, i_N, \qv)
$$ (eq-objectgenericode1-eom)

Note that the user function $\fv_{user}(mbs, t, i_N, \qv)$ may be empty (=0), and that `iN` represents the itemNumber (=objectNumber).

CoordinateLoads are added for the respective {ref}`ODE1 <ODE1>` coordinate on the RHS of the latter equation.

### Marker interfaces

The object is no body: markers act on its coordinates only, `MarkerNodeODE1Coordinate` on a
coordinate of one of its nodes, e.g. for a `LoadCoordinate` - which adds to the right-hand side of
that coordinate's equation - or a coupling to a mechanical system in a user function.

*Example*:

```python
A = numpy.diag([200,100])
#simple linear user function returning A*q + const
def UFrhs(mbs, t, itemNumber, q):
    return np.dot(A, q) + np.array([0,2])

nODE1 = mbs.AddNode(NodeGenericODE1(referenceCoordinates=[0,0],
                                    initialCoordinates=[1,0], numberOfODE1Coordinates=2))

#now add object instead of object in mini-example:
oGenericODE1 = mbs.AddObject(ObjectGenericODE1(nodeNumbers=[nODE1],
                   rhsUserFunction=UFrhs))

```

**Userfunction**: `rhsUserFunction(mbs, t, itemNumber, q)`
A user function, which computes a RHS vector depending on current time and states of the object.
Can be used to create any kind of first order system, especially state space equations (inputs are added via CoordinateLoads to every node).
Note that itemNumber represents the index of the ObjectGenericODE1 object in mbs, which can be used to retrieve additional data from the object through
`mbs.GetObjectParameter(itemNumber, ...)`, see the according description of `GetObjectParameter`.

| arguments / return | type or size | description |
|---|---|---|
| `mbs` | MainSystem | provides MainSystem mbs to which object belongs |
| `t` | Real | current time in mbs |
| `itemNumber` | Index | integer number $i_N$ of the object in mbs, allowing easy access to all object data via mbs.GetObjectParameter(itemNumber, ...) |
| `q` | Vector $\in \Rcal^n$ | object coordinates (composed from {ref}`ODE1 <ODE1>` nodal coordinates) in current configuration, without reference values |
| **return value** | Vector $\in \Rcal^{n}$ | returns force vector for object |

(miniexample-objectgenericode1)=
## Mini example


```python
#set up a 2-DOF system
nODE1 = mbs.AddNode(NodeGenericODE1(referenceCoordinates=[0,0],
                                    initialCoordinates=[1,0],
                                    numberOfODE1Coordinates=2))

#build system matrix and force vector
#undamped mechanical system with m=1, K=100, f=1
A = np.array([[0,1],
              [-100,0]])
b = np.array([0,1])

oGenericODE1 = mbs.AddObject(ObjectGenericODE1(nodeNumbers=[nODE1], 
                                               systemMatrix=A, 
                                               rhsVector=b))

#assemble and solve system for default parameters
mbs.Assemble()

sims=exu.SimulationSettings()
solverType = exu.DynamicSolverType.RK44
mbs.SolveDynamic(solverType=solverType, simulationSettings=sims)

#check result at default integration time
exu.sys['testResult'] = mbs.GetNodeOutput(nODE1, exu.OutputVariableType.Coordinates)[0]
```


Relevant Examples (Ex) and TestModels (TM) with weblink to github: [`HydraulicsUserFunction.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/Examples/HydraulicsUserFunction.py) (Ex), [`lugreFrictionODE1.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/Examples/lugreFrictionODE1.py) (Ex), [`lugreFrictionTest.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/Examples/lugreFrictionTest.py) (Ex), [`genericODE1duplicateNodeTest.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/TestModels/genericODE1duplicateNodeTest.py) (TM), [`solverExplicitODE1ODE2test.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/TestModels/solverExplicitODE1ODE2test.py) (TM), [`taskmanagerTest.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/TestModels/taskmanagerTest.py) (TM)