1.3 Notations, Sign Conventions, and Degrees of Freedom

A vibrating mass block can be characterized by 6 defrees of freedom, 3 translational (u,v,w) and 3 rotational (ζ,η,Ψ) as depicted in Figure 1.3.1.

Figure 1.3 Sign conventions and degrees of freedom notations

The table below provides a summary for the 6 degrees of freedom.

The positive values are shown in the diagram, translations are in the positive axis direction and the rotations are following the right hand rule (rotation direction is such that your right thumb is pointing toward the positive axis while your remaining fingers are rotating around the axis).

In practice, these motions don’t happen independently, they can be coupled with each other. The most common coupled motion that was studied analytically in the literature is the coupled horizontal and rocking motion where the rigid body can move horizontally and rotate at the same time.

Observations