# Definition: Frame of Reference

Let $$\mathcal R=(\mathbb R,V_{\mathbb R},v)$$ be the $$3$$-dimensional affine space with the associated normed vector space $$(V_{\mathbb R},||~||)$$ over the field of real numbers $$\mathbb R$$. Any non-empty affine bounded subset $$\mathcal I\subset\mathcal R$$ is also called a frame of reference.

### Practical Consequences from this Definition

Please note that any frame of reference $$\mathcal I$$ has a norm $$||~||$$ induced by the associated vector space, i.e. we can measure the distance between any two points $$P,Q\in\mathcal I$$ by measuring the norm of the corresponding vector $||\overrightarrow{PQ}||\ge 0\in\mathbb R.$

Please also note that the boundedness of $$\mathcal I$$ is chosen in the definition for technical reasons to avoid the necessity to deal with infinite (unbounded) frames of reference to model the physics of real world.

### Examples

Frames of reference can be:

• $$0$$ dimensional (e.g. a particle)
• $$1$$ dimensional (e.g. being a gravitational model of a binary star system)
• $$2$$ dimensional (e.g. a (bounded) surface of the Earth small enough to ignore the Earths curvature)
• $$3$$ dimensional (e.g. a vehicle, a spaceship, a light clock, etc.)

Definitions: 1

Thank you to the contributors under CC BY-SA 4.0!

Github:

### References

#### Bibliography

1. Piotrowski, Andreas: Own Research, 2014