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$$$$ IMPE     NOTICE  BP208322  13/05/23    21:15:10     7774           
                                             DATE     13/05/23

     Operateur IMPE :     Voir aussi: MASS, RIGI, AMOR , CORIOLIS, GYRO
     ---------------                                     
 
      RIG1 = IMPE RIG2 (RIG3) (REEL1) (| 'MASSE'            | )  (FLAM); 
                                       | 'RAIDEUR'          |  
                                       | 'AMORTISSEMENT'    |  
                                       | 'QUELCONQUE'  LISREEL1  |  
  

Objet:
------ 
  


 
  The IMPEDANCE operator computes the impedance matrix (or dynamic 
  stiffness) (of subtype MASSE, RAIDEUR or AMORTISSEMENT)  
                                                            

  INPUT :
  -------  
  
  RIG2: Initial stiffness matrix with primal and dual unknows in the
        temporel domain (UX, UY, ..., FX, FY, ...)

  REEL1: REEL corresponding to the pulsation (unit: rad/s) for which 
         is computed the impendance matrix (by default: 1 rad/s)
      
  FLAM: LOGIQUE (FAUX by default) specifying if the matrix has a MASS 
        type (necessary for the buckling analysis)  

  'MASSE', 'RAIDEUR', 'AMORTISSEMENT', 'QUELCONQUE': Key word giving 
  the type of IMPENDANCE matrix to be calculated

  The option 'QUELCONQUE' requires a list of real LISREEL1 with 4 real:
  LISREEL1 = PROG REELA REELB REELC REELD;  

  2 matrices can be fournish as input in order to couple their dof of
  common name. It is for example the case when one wants to couple
  symmetric and antisymmetric displacement in 2D-Fourier modeling 
  (e.g. in rotor modeling) with:
  - RIG2 which is the matrix corresponding to symmetric dofs 
    (obtained after the instruction OPTION MODE FOUR nhar;)
  - RIG3 which is the matrix corresponding to antisymmetric dofs 
    (obtained after the instruction OPTION MODE FOUR (-1*nhar);)

  Only the RAIDEUR option is permitted when the input matrice contains
  some relationship (e.g. with Lagrange multiplier LX).
  

  OUTPUT :
  --------

  RIG2: RIGIDITE object describing the impedance matrix (with the same
        subtype as the input matrice or with the MASSE subtype if 'FLAM'
        is precised.
        
  RIG2 is created by duplication of the RIG1 matrix on the imaginary
  degrees of freedom  (IUX, IUY, ..., IFX, IFY, ...) with the following 
  rules:

  Keyword 'RAIDEUR':     [  RIG1    0   ]
                         [   0     RIG1 ]

  Keyword 'MASSE':       [ -REEL1^2*RIG1         0     ]
                         [       0       -REEL1^2*RIG1 ]

  Keyword 'AMORTISSEMENT':   [      0     -REEL1*RIG1 ]
                             [ REEL1*RIG1      0      ]


  Keyword 'QUELCONQUE':  [ REELA*RIG1     REELB*RIG1 ]
                         [ REELC*RIG1     REELD*RIG1 ]


  In the case of 2 input matrices, RIG1 is built as:
  
  Keyword 'RAIDEUR':     [  RIG2    0   ]
                         [   0     RIG3 ]

  Keyword 'MASSE':       [ -REEL1^2*RIG2         0     ]
                         [       0       -REEL1^2*RIG3 ]

  Keyword 'AMORTISSEMENT':   [      0     -REEL1*RIG2bar ]
                             [ REEL1*RIG3bar      0      ]

  with RIG2bar_{ij} = | - RIG2_{ij}  if j refers to UT dof
                      |   RIG2_{ij}  for all other dofs