# Node SwimSpeedNode

Defined in `mime.nodes.body._swim_speed.SwimSpeedNode`.

Algorithm `MIME-NODE-115`.

A body's velocity along a direction each step, and its mean over the steps that end after a start time, kept in the node's own state.

## Governing equations

$$
s = \mathbf{v} \cdot \mathbf{e}, \quad D = \sum_{k : t_{k} > t_{a}} s_{k} \, h, \quad T = \sum_{k : t_{k} > t_{a}} h, \quad \bar{s} = D / T
$$

## 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 body's velocity read at a step holds over that step, so the distance is the sum of the speed times the timestep
- The time of a step is its count times the timestep, and a step counts whole once its end lies after the start time

## Limitations

- The window's edge is a switch: the distance and the time observed move in jumps of a step as the start time moves, and the mean is zero until some time has been observed

## Declared regimes (not evidenced here)

none declared

## References

none declared

## Symbols

| Symbol | Kind | Name | Units | Implemented by |
|---|---|---|---|---|
| $s$ | state | `speed` | m/s | `mime.nodes.body._swim_speed.SwimSpeedNode.advance` |
| $D$ | state | `distance` | m | `mime.nodes.body._swim_speed.SwimSpeedNode.advance` |
| $T$ | state | `observed` | s | `mime.nodes.body._swim_speed.SwimSpeedNode.advance` |
| $\bar{s}$ | state | `mean_speed` | m/s | `mime.nodes.body._swim_speed.SwimSpeedNode.advance` |
| $\mathbf{v}$ | input | `twist` | m/s; rad/s | `mime.nodes.body._swim_speed.SwimSpeedNode.advance` |
| $\mathbf{e}$ | parameter | `along` | 1 | `mime.nodes.body._swim_speed.SwimSpeedNode.advance` |
| $t_{a}$ | parameter | `after` | s | `mime.nodes.body._swim_speed.SwimSpeedNode.advance` |

## Built by

- [`swim_speed`](../entries/observation/swim_speed.md) 0.1.0