# Node SourceReactionNode

Defined in `mime.nodes.actuation._reaction.SourceReactionNode`.

Algorithm `MIME-NODE-111`.

The reaction of a law's wrench on a body, on the source it reads: equal and opposite, its torque moved to the origin of the frame the source is mounted on.

## Governing equations

$$
\mathbf{W}_{k} = \begin{bmatrix} -\mathbf{F} \\ -\boldsymbol{\tau} - (\mathbf{c} - \mathbf{o}_{k}) \times \mathbf{F} \end{bmatrix}
$$

## Discretisation

none declared; a node whose order depends on its construction declares it with the `discretization_order()` hook, which is read from a built node.

## Assumptions

- The law's force on the body and its reaction on the source are equal and opposite and act along one line, as between two point dipoles

## Limitations

none declared

## Declared regimes (not evidenced here)

none declared

## References

[@Jackson1998]

## Symbols

| Symbol | Kind | Name | Units | Implemented by |
|---|---|---|---|---|
| $\mathbf{W}$ | state | `link_wrench` | N; N m (units declared, not checked) | `mime.nodes.actuation._reaction.SourceReactionNode.advance` |
| $\mathbf{F}$ | input | `wrench` | N; N m | `mime.nodes.actuation._reaction.SourceReactionNode.advance` |
| $\boldsymbol{\tau}$ | input | `wrench` | N; N m | `mime.nodes.actuation._reaction.SourceReactionNode.advance` |
| $\mathbf{c}$ | input | `pose` | m; 1 | `mime.nodes.actuation._reaction.SourceReactionNode.advance` |
| $\mathbf{o}$ | input | `mount_poses` | m; 1 | `mime.nodes.actuation._reaction.SourceReactionNode.advance` |

A row marked *units declared, not checked* has the units its author wrote: the code declares none there, so the node walk cannot compare them with anything.

## Built by

- [`magnetic.force`](../entries/interaction/magnetic.force.md) 0.1.0
- [`magnetic.torque`](../entries/interaction/magnetic.torque.md) 0.1.0