Frame of Reference

reference frame

 or frame of reference

Coordinate system that allows description of time and position of points relative to a body. The axes, or lines, emanate from a position called the origin. As a point moves, its velocity can be described in terms of changes in displacement and direction. Reference frames are chosen arbitrarily. For example, if a person is sitting in a moving train, the description of the person's motion depends on the chosen frame of reference. If the frame of reference is the train, the person is considered to be not moving relative to the train; if the frame of reference is the Earth, the person is moving relative to the Earth.

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frame of reference

Geometry any set of planes or curves, such as the three coordinate axes, used to locate or measure movement of a point in space

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frame of reference [¦frām əv ′ref·rəns]

(physics)

A coordinate system for the purpose of assigning positions and times to events. Also known as reference frame.

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Frame of reference

A base to which to refer physical events. A physical event occurs at a point in space and at an instant of time. Each reference frame must have an observer to record events, as well as a coordinate system for the purpose of assigning locations to each event. The latter is usually a three-dimensional space coordinate system and a set of standardized clocks to give the local time of each event. For a discussion of the geometrical properties of space-time coordinate systems See Space-time, Relativity

In the ordinary range of experience, where light signals, for all practical purposes, propagate instantaneously, the time of an event is quite distinct from its space coordinates, since a single clock suffices for all observers, regardless of their state of relative motion. The set of reference frames which have a common clock or time is called newtonian, since Isaac Newton regarded time as having invariable significance for all observers.

For discussion of other types of reference frames.

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Frame of Reference 

in mechanics, the aggregate of a system of coordinates and clocks associated with a body, in reference to which the motion or equilibrium of any other mass points or bodies is being studied. Any motion is relative, and the motion of a body must be examined in relation to some other body—the reference body—or to a system of bodies. For example, it is not possible to describe the motion of the moon in a general way; it is only possible to determine the motion in relation to the earth or the sun and the stars or some other heavenly body.

Mathematically, the motion of a body or mass point in relation to a chosen frame of reference is described by equations. The equations state how the coordinates defining the position of the body or point in a frame of reference change with the passage of time t. For example, if the Cartesian coordinates x, y, z are used, the motion of a point is determined by the equations x = f₁(t), y = f₂(t), z = f₃(t). These equations are called equations of motion (seeKINEMATICS).

The choice of a frame of reference depends on the purpose of the investigation. In kinematic investigations, all frames of reference are equally valid. In problems in dynamics, inertial reference frames are preferred, for which differential equations of motion usually assume a simpler form.

REFERENCES

Khaikin, S. E. Fizicheskie osnovy mekhaniki. Moscow, 1963. Sections 7 and 16.
Aizerman, M. A. Klassicheskaia mekhanika. Moscow, 1974. Chapter 1, sec. 1; ch.2, sec.2.

S. M. TARG