November 15, 2012
The Selection of State Variables
When dealing with multi-body systems, it matters greatly, which variables are being selected as state variables, as this will influence strongly the efficiency of the generated simulation code.
If we choose our state variables wisely, the number of simulation equations of a tree-structured multi-body system grows linearly in the number of degrees of freedom.
If we make a poor choice of our state variables, the number of run-time equations grows with the fourth power of the number of degrees of freedom.
To this end, we should use the relative positions and velocities of joints as our preferred state variables.