information:classification
Kinematics: motion and deformation

A change in the configuration of a continuum body results in a displacement. The displacement of a body has two components: a rigid-body displacement and a deformation. A rigid-body displacement consists of a simultaneous translation and rotation of the body without changing its shape or size. Deformation implies the change in shape and/or size of the body from an initial or undeformed configuration κ 0 (B) {\displaystyle \kappa _{0}({\mathcal {B}})} to a current or deformed configuration κ t (B) {\displaystyle \kappa _{t}({\mathcal {B}})} (Figure 2).

The motion of a continuum body is a continuous time sequence of displacements. Thus, the material body will occupy different configurations at different times so that a particle occupies a series of points in space which describe a path line.

There is continuity during motion or deformation of a continuum body in the sense that:

It is convenient to identify a reference configuration or initial condition which all subsequent configurations are referenced from. The reference configuration need not be one that the body will ever occupy. Often, the configuration at t = 0 {\displaystyle t=0} is considered the reference configuration, κ 0 (B) {\displaystyle \kappa _{0}({\mathcal {B}})}. The components X i {\displaystyle X_{i}} of the position vector X {\displaystyle \mathbf {X} } of a particle, taken with respect to the reference configuration, are called the material or reference coordinates.

When analyzing the motion or deformation of solids, or the flow of fluids, it is necessary to describe the sequence or evolution of configurations throughout time. One description for motion is made in terms of the material or referential coordinates, called material description or Lagrangian description.