README NOTE ON DMAP ALTER PACAKGE FOR REPEATABLE RIGID BODY MODES USING 
LANCZOS METHOD, rnormal.v707

M. A. Gockel, January 14, 2000

1. BACKGROUND.  
   
   The LAN and AHOU methods both start with random numbers when 
   generating eigenvectors.  Rigid body modes are a special case of repeated roots.
   Eigenvectors for repeated roots are not unique.  They tend to change for small
   changes in the model, or even for changing solution parameters such as the 
   number of initial vectors ("blocksize" on the eigrl entry). The AHOU method 
   allows the user to make the rigid body roots repeatable by use of the SUPORT 
   entry.  The SUPORT entry is not used for this purpose in the LAN method at 
   present.  The alter allows the LAN method to also provide repeatable 
   eigenvectors, using the same equations as the AHOU method in DMAP steps 
   made after the eigensolution.  

2. INPUT.  
 
   Place "include 'rnormal.v707'" before the cend entry.  Any eigensolution 
   method requested will be replaced by the LAN method.  PARAM, RNRATIO, [real] 
   is used to distinguish zero roots with computational zero values from low 
   frequency roots.  Its default value of 1.E6 is perhaps too tolerant when you 
   expect modeling errors to cause spurious low frequency roots.  A larger value 
   makes it less tolerant.

3. OUTPUT.  

   Output is conventional.  New messages list the number of rigid body modes 
   found in the eigensolver.  A fatal message is produced when the number,
   as determined from inspecting eigenvalues, is not the same listed on SUPORTi 
   entries.  The theory used is described in a TAN, in preparation.

4. EXAMPLE PROBLEM.  File rnormal1.dat is the input file for a small straight 
   shaft whose mass has been tuned such that all 6 diagonal terms of the rigid 
   body mass are unity.  This is the most difficult type of problem for which 
   to generate repeatable rigid body eigenvectors.  It is a modal frequency 
   response model.  If you compare its results with the same model when the 
   alter package is removed you will find that the physical results 
   (ACCELERATION) are identical, but that the modal results (SDISPL) differ 
   greatly.  If the same small change is made to both models the results without 
   the alter will change greatly, but the results with the alter should change 
   only a small amount.