# Rest system

The rest system of a rigid body is a frame of reference in which it rests, i.e. H. in which all of its coordinates remain constant. If the coordinate origin is in the center of gravity of the body, it is also a center of gravity system for this.

In a more general formulation, the rest system of a physical system S is the frame of reference in which the total momentum of S is zero.

For a body free of forces, a rest system is an inertial system . In general, however, inertial forces occur, so a rest frame is generally an accelerated frame of reference .

For example, the rest system of the earth's surface rotates with the earth's rotation, which leads to centrifugal and Coriolis forces , with a clear influence (among other things) on ocean currents and climate.

## Rest systems as an observer in the special theory of relativity

Systems of rest of points are called observers in the special theory of relativity . The time that passes for the observer is called proper time . The relationships between objects that are at rest relative to one another are used directly to define the measured variables distance and duration and consequently indirectly to define the measured variables based on them such as speed , acceleration , angle , angular velocity , curvature , etc.

## Observer in general relativity

In the general theory of relativity , “observer” denotes curves on spacetime , the derivation of which is time-like everywhere . At each point of the curve, the general theory of relativity can be approximated by the special one, then one obtains momentarily moving reference frames (MCRF).

## Restricted rest systems and their relationships

The requirement for mutual calm can be met by those involved who establish relationships with one another that go beyond this, e.g. B. that each four of them among themselves just are. The corresponding rest system in such a case represents a (subset of a) level. The members of different such rest systems in turn do not necessarily rest to one another, or they do not necessarily move vis-à-vis one another (uniformly or differently), but there is also the possibility that they are rigid to each other .

## Establishment of inertial systems based on given rest systems

If the members of a given rest system (or their displays) are assigned coordinate values ​​and these are affine with respect to the existing distances (or durations), the coordinate system thus formed is called an inertial system.