Frame of reference ↩

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shorthands: {}
aliases: [Reference frame]
created: 2022-01-13 13:31:46
modified: 2022-01-14 13:15:20

We can describe the motion of a body in different frames of reference. The reference frame is, in some sense, the "Euclidean space carried by the observer".

A more mathematical definition: the reference frame is the set of all points in the Euclidean space with the rigid body motion of the observer. The frame, denoted , is said to move with the observer.

The positions of particles are labeled relative to a frame by establishing a coordinate system with origin . The corresponding set of axes, sharing the rigid body motion of the frame , can be considered to give a physical realization of . In a frame , coordinates are changed from to by carrying out, at each instant of time, the same coordinate transformation on the components of intrinsic objects (vectors and tensors) introduced to represent physical quantities in this frame.¹

Distinction from coordinate system

The idea of reference frames and coordinate systems might seem similar, but is quite different.

We get different frames by defining different spaces or times, so the ideas of a space, a time, of rest and simultaneity, go inextricably together with that frame.
A shift of origin or a spatial rotation results in a new coordinate system.

So frames correspond to at best classes of coordinate systems.²

Salençon, J. (2001). Handbook of continuum mechanics: General concepts, thermoelasticity. Springer. Link
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Nerlich, G., Nerlich, P. P. G., Press, C. U., & Graham, N. (1994). What Spacetime Explains: Metaphysical Essays on Space and Time. Cambridge University Press. Link
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