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Jack H

12.1 BASICS

When we deal with geometries in two dimensions we have three position variables (dof) for each rigid body (two for position, one for orientation).

When a problem is expanded to three dimensions we then have six position variables (dof) for a rigid body (three for position, and three for orientation).

These added degrees of freedom expand the complexity of the problem solutions. There are a few potential approaches,

-look for regularities that simplify the problem (scalar)

-vector based approaches (positions)

-matrix based approaches (positions and orientations)

Consider the example of the spherical joint - all of the axes of rotation coincide.