In certain cases it is desirable to add additional degrees of freedom to compute particle mass, temperature, size, spin, and so forth. The additional degree of freedom is solved for each particle. For each degree of freedom, w, the following ODE is solved for each particle:

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

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