Dynamical Description of Elastic Bodies

Abstract

For the kinematic description of an elastic body two coordinate systems are introduced, see Fig. 2.1-1. On the one hand the inertia I-coordinate system, which is fixed in space and on the other hand the R-coordinate system, which is fixed to the elastic body at the point R. These two coordinate systems are usually used to describe in the limiting case the rigid body dynamics. Here, the elastic deformations are introduced additionally to describe the kinematics of an elastic body. Both coordinate systems are related by

$$ _I\overrightarrow e =^{IR}{A_R}\overrightarrow e$$

((2.1-1))

with the orthogonal transformation matrix ^IRA with the properties

$$^{RI}{A^{IR}}A = E$$

((2.1-2))

and

$$^{IR}{A^T} = ^{RI}A$$

((2.1-3))

.