Continuum Mechanics and Theory of Materials pp 155-176 | Cite as

# Objectivity

## Abstract

In kinematics the current configuration of a material body is identified with an area of the three-dimensional Euclidean space of physical observation. In this way the material body is embedded in the Euclidean structure of the observation space. In particular, the points P∈E^{3}, where the material points *p*∈*R* are currently located, are characterised by position vectors *x*∈V^{3}. In order to establish a one-to-one relation between point P and vector *x*, it is necessary to introduce a *reference system* or *frame of reference.* ^{1} There are any number of possibilities for achieving this, i.e. the choice of a special reference system is always linked to a certain arbitrariness. However, we have to take into consideration what we have learned from experience, that balance relations of mechanics do not apply in the same way for all reference frames: the balance relations for linear momentum and rotational momentum refer to *inertial frames.* ^{2} An inertial frame is a reference system with the property that conclusions drawn from the balance relations of linear and rotational momentum correspond to results obtained in practical experiments. An example is the law of inertia, from the validity of which the term *inertial frame* is derived. Experience shows that there are reference frames that can be regarded in good approximation as inertial frames within the measuring accuracy available. Once one has found an inertial frame, then all frames that move at a constant velocity and without rotation with respect to this reference system are also inertial frames: the basic equations of classical mechanics are invariant with respect to *Galilei* transformations. A *Galilei* transformation is a transformation between two frames of reference, related to each other by a translational motion with constant velocity. Once an inertial frame is known, the balance equations can be applied to any reference system which is not an inertial frame. In order to do so, however, it is imperative to know how the fields that appear in the balance relations transform when the frame of reference is changed. In this connection a certain transformation behaviour is denoted by the term objectivity.

### Keywords

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