Basic Kinematics

Abstract

In the preceding chapter, we discussed the geometric properties of the present configuration κ _t under the assumption that the parameter t describing temporal changes of the body is kept fixed. That is, the motion function $\vec \chi$ is considered to be a deformation map $\vec \chi (\cdot ,t)$. Now, we turn our attention to the problem in the case of motion, that is, where the function $\vec \chi$ is treated as the map $\vec \chi (\vec X,\cdot )$ for a fixed point $\vec X$. We assume that the mapping $\vec \chi (\vec X,\cdot )$ is twice differentiable.