Equation of the Center of Mass in Fortran language

The Fortran implementation of the equation of the Center of Mass is divided in three parts:

• the main program that calls the subroutine for the calculation of the center of mass;
• the subroutine that calculates X and Y coordinates of the center of mass of a plane region;
• the subroutine that calculates slopes and y-intercepts of a plane region.

Example of main program

C!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
C
C PROGRAM : something
C
C Description : Program that...
C
C!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
C
C Variables:  SIZE : Number of coordinates in the plane region
C             XY   : X and Y coordinates of the plane region
C             CTR  : X and Y coordinates of the center of mass
C
C!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 
      PROGRAM something
 
      IMPLICIT NONE
 
      INTEGER*2 SIZE
      REAL*4 XY(2,18000), CTR(2)
 
      SIZE = 4
 
      XY(1,1) = 543564
      XY(2,1) = 5678654
      XY(1,2) = 543735
      XY(2,2) = 5678943
      XY(1,3) = 543423
      XY(2,3) = 5678679
      XY(1,4) = 543564
      XY(2,4) = 5678654
 
      CALL CENTROID(SIZE, XY, CTR)
 
      PRINT *,CTR(1)  ! Display the X coordinate of the center of mass
      PRINT *,CTR(2)  ! Display the Y coordinate of the center of mass
 
      STOP
      END
    

Subroutine that calculates the X and Y coordinates of the center of mass of a plane region

C!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
C
C ROUTINE : CENTROID
C
C Description : This subroutine returns the center of mass of a plane region
C               using vectors (SLOPE), y-interceps (YINTER),
C               X-beginning and X-ending coordinates (X1, X2).
C
C!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
C
C Input variables:   SIZE   : Number of coordinates in the plane region
C                    XY     : X and Y coordinates of the plane region
C
C Output variables:  CTR    : X and Y coordinates of the center of mass
C
C Arguments :        SLOPE  : Vector of slopes
C                    YINTER : Vector of y-intercepts
C                    X1     : X coordinate of the beginning of a linear segment
C                    X2     : X coordinate of the end of a linear segment
C
C!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 
      SUBROUTINE CENTROID (SIZE, XY, CTR)
 
      IMPLICIT NONE
 
      INTEGER*2 SIZE, I
      REAL*4 XY(2,18000), CTR(2)
      REAL*8 X1(18000), X2(18000)
      REAL*8 SLOPE(18000), YINTER(18000)
      REAL*8 M1, M2, M3, MX, MY, A, SUMA, SUMMX, SUMMY
 
C Beginning of process
 
      SUMA  = 0.0D0
      SUMMX = 0.0D0
      SUMMY = 0.0D0
 
      CALL SLOPE_YINTER ( SIZE, XY, SLOPE, YINTER, X1, X2)
 
      DO I = 1,SIZE-1
         M3   = (X2(I)**3)-(X1(I)**3)
         M2   = (X2(I)**2)-(X1(I)**2)
         M1   = X2(I)-X1(I)
         MX   = ((SLOPE(I)**2)*M3/6) + (((YINTER(I)*SLOPE(I))*M2)/2) + (((YINTER(I)**2)*M1)/2)
         MY   = ((SLOPE(I)*M3)/3)+((YINTER(I)*M2)/2)
         A    = ((SLOPE(I)/2)*M2)+(YINTER(I)*M1)
        SUMA  = SUMA + A
        SUMMX = SUMMX + MX
        SUMMY = SUMMY + MY
      END DO
 
C Calculation of the center of mass
 
      CTR(1) = SUMMY/SUMA    ! X coordinate of the center of mass
      CTR(2) = SUMMX/SUMA    ! Y coordinate of the center of mass
 
      RETURN
      END
    

Subroutine that calculates the slopes and y-intercepts of a plane region

C!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
C
C ROUTINE: SLOPE_YINTER
C
C Description: This subroutine returns a vector that contains the slopes and
C              y-intercepts on the x-axis for all the segments of a plane region.
C
C!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
C
C Input variables:   SIZE   : Number of coordinates in the plane region
C                    XY     : X and Y coordinates of the plane region
C
C Output variables:  SLOPE  : Vector of slopes
C                    YINTER : Vector of y-intercepts
C                    X1     : X coordinate of the beginning of a linear segment
C                    X2     : X coordinate of the end of a linear segment
C
C Arguments:         I      : Counter of coordinates
C                    X1     : X coordinate of the beginning of a linear segment
C                    X2     : X coordinate of the end of a linearsegment
C
C!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 
      SUBROUTINE SLOPE_YINTER ( SIZE, XY, SLOPE, YINTER, X1, X2 )
 
      IMPLICIT NONE
 
      INTEGER*2 SIZE, I
      REAL*4 XY(2,18000)
      REAL*8 X1(18000), X2(18000), Y1(18000), Y2(18000), SLOPE(18000), YINTER(18000)
 
C Extracting the coordinates of the plane region
 
      DO I = 1, SIZE-2
         X1(I) = XY(1,I)
         Y1(I) = XY(2,I)
         X2(I) = XY(1,I+1)
         Y2(I) = XY(2,I+1)
      END DO
 
      X1(SIZE-1) = XY(1,SIZE-1)
      Y1(SIZE-1) = XY(2,SIZE-1)
      X2(SIZE-1) = XY(1,1)
      Y2(SIZE-1) = XY(2,1)
 
C Calculating slopes and y-intercepts
 
      DO I = 1, SIZE-1
         IF (X1(I) .EQ. X2(I)) THEN
            SLOPE(I) = 0.
            ORD(I) = 0.
         ELSE
            SLOPE(I) = (Y2(I) - Y1(I)) / (X2(I) - X1(I))
            YINTER(I) = ((X1(I) * Y2(I)) - (X2(I) * Y1(I))) / (X1(I) - X2(I))
         END IF
      END DO
 
      RETURN
      END