# Participation Factor And Effective Mass
The modal mass for mode
The direction information can be extracted using the participation
factor. The participation factor for mode
The rigid body vectors are defined as
So a rigid body vector for a rotation of
The effective mass in a rotated axis system can be calculated from the participation factors and effective masses.
The sum of the effective mass in any given direction over all the modes is the total unrestrained mass. Staring with the definition of effective mass
The rigid body vector can be written as
So the term in the numerator of the effective mass becomes
Also the total mass
So the sum of the effective masses over all the modes is the total unrestrained mass.