# Node MagneticTorqueNode

Defined in `mime.nodes.magnetic._torque.MagneticTorqueNode`.

Algorithm `MIME-NODE-114`.

The torque of a magnetic field on a body's permanent moment, tau = m x B, as a wrench about the centre of mass with no force.

## Governing equations

$$
\boldsymbol{\tau} = \mathbf{m} \times \mathbf{B}, \quad \mathbf{m} = R(\mathbf{q}) \, \mathbf{m}_{b}
$$

## 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

- A point dipole with a rigid, permanent moment fixed in the body
- The field is read at the body's centre of mass: it is taken uniform across the body
- The body's orientation is the one read at the start of the step, so the torque of a step turns the body as it stood after the step before

## Limitations

none declared

## Declared regimes (not evidenced here)

none declared

## References

[@Ling2016UniversityPhysics2]

## Symbols

| Symbol | Kind | Name | Units | Implemented by |
|---|---|---|---|---|
| $\boldsymbol{\tau}$ | state | `wrench` | N; N m | `mime.nodes.magnetic._torque.MagneticTorqueNode.advance` |
| $\mathbf{B}$ | input | `flux_density` | T | `mime.nodes.magnetic._torque.MagneticTorqueNode.advance` |
| $\mathbf{m}_{b}$ | parameter | `moment` | A m^2 | `mime.nodes.magnetic._torque.MagneticTorqueNode.advance` |
| $\mathbf{q}$ | input | `pose` | m; 1 | `mime.nodes.magnetic._torque.MagneticTorqueNode.advance` |

## Built by

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