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(sec-item-nodepoint2d)=
# NodePoint2D

A 2D point node for point masses or solid finite elements which has 2 displacement degrees of freedom for {ref}`ODE2 <ODE2>`.

## Interface

- Python names: `NodePoint2D` or `Point2D`, and `VPoint2D` for its visualization
- Provides: `Position2D`
- Node markers that can be attached: [](#sec-item-markernodeposition)
- Objects that take this node: [](#sec-item-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](#sec-drawing-nodes).

## 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 |
|---|---|---|
| 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) |

(description-nodepoint2d)=
## Detailed description

### Coordinates

| index | symbol | kind | meaning | frame |
|---|---|---|---|---|
| 0, 1 | $q_0,\,q_1$ | {ref}`ODE2 <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 {ref}`ODE2 <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 [](#sec-item-objectmasspoint2d)

(miniexample-nodepoint2d)=
## Mini example


```python
#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`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/Examples/pendulum2Dconstraint.py) (Ex), [`SliderCrank.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/Examples/SliderCrank.py) (Ex), [`SpringDamperMassUserFunction.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/Examples/SpringDamperMassUserFunction.py) (Ex), [`slidercrankWithMassSpring.py`](https://github.com/jgerstmayr/EXUDYN/blob/master/python/Examples/slidercrankWithMassSpring.py) (Ex)