Invariant variables

RecurDyn RFlex has the 9 invariant variables as follows.

1.  Invariant variable M1:  (1x1)

2.  Invariant variable M2:  (3x1)

3.  Invariant variable M3:  (3x3)

4.  Invariant variable N1:  j=1, nM ((3x1)x nM)

5.  Invariant variable N2:  j=1, nM ((3x3)x nM)

6.  Invariant variable N3:  j=1, nM ((3x3)x nM)

7.  Invariant variable N4:  j,k=1, nM ((3x3)x nM x nM)

8.  Invariant variable N5:  j=1, nM ((3x1)x nM)

9.  Invariant variable N6:   j,k=1, nM ((3x1)x nM x nM)

Where,

 is a lumped mass of p node.

  is a position vector of p node with respect to RFlex body reference frame.

 is a moment of inertia of p node with respect to RFlex body reference frame.

 and  are translation and rotational mode shape with j-th mode of p node.

nM is number of modes.

①  Mass matrix for RFlex body is defined as follows using the RD/RFlex Invariant variables. (r : translational DOF, w : rotational DOF, a : modal coordinates)

②  Mass center position of RFlex body

Where,

  and   are a position vector and an orientation matrix of the RFlex body in a simulation time, respectively.

 is the modal coordinate vector in a simulation time.