In certain cases, it is desirable to add degrees of freedom to the grains. You can do so by using the Auxiliary Dependent Variable feature. The additional degrees of freedom are solved for each grain. For each degree of freedom, w, the following ODE is solved for each grain:

where R is a user-defined source term. When the Integrate option is set to Along grain trajectory, the following ODE is solved for each grain instead:

where s (SI unit: m) is the direction tangential to the motion of the grain.