perm filename PAGE51[00,BGB] blob sn#047833 filedate 1973-06-07 generic text, type T, neo UTF8
~F8SUMMARY OF LAMINA INERTIA TENSOR EXPRESSIONS.

RECTANGLE'S  LAMINA INERTIA TENSOR ABOUT ITS CENTER OF MASS.

	MXX	←	B*B*AREA/12;		(B HEIGHT IN ROWS).
	MYY 	←	A*A*AREA/12;		(A WIDTH IN COLUMNS).
	MZZ	←	MXX + MYY;
	PXY 	←	0;

ORIENTED RIGHT TRIANGLE'S LAMINA INERTIA TENSOR ABOUT ITS CENTER OF MASS.

	MXX	←	B*B*AREA/18;		(B HEIGHT IN ROWS).
	MYY	←	A*A*AREA/18;		(A WIDTH IN COLUMNS).
	MZZ	←	MXX + MYY;
	PXY	←	-A*B*AREA/36;

SUMMATION OF LAMINA INERTIA TENSORS.

	AREA	←	(AREA1  +  AREA2);
	XCM	←	(AREA1 * XCM1  +  AREA2 * XCM2) / AREA;
	YCM	←	(AREA1 * YCM1  +  AREA2 * YCM2) / AREA;
	MXX	←	MXX1 + YCM1*YCM1*AREA1  +
			MXX2 + YCM2*YCM2*AREA2  -  YCM*YCM*AREA;
	MYY	←	MYY1 + XCM1*XCM1*AREA1  +
			MYY2 + XCM2*XCM2*AREA2  -  XCM*XCM*AREA;
	PXY	←	PXY1 - XCM1*YCM1*AREA1  +
			PXY2 - XCM2*YCM2*AREA2  +  XCM*YCM*AREA;

ANGLE OF PRINCIPLE AXIS

	PHI	←	0.5*ATAN((MYY-MXX)/(2*PXY))
	PXY	←	0.5*(MYY - MXX)*TAN(2*PHI)

TRANSLATION OF LAMINA INERTIA TENSOR AWAY FROM CENTER OF MASS.
	
	MXX'	←	MXX  +  AREA*DY*DY;
	MYY'	←	MYY  +  AREA*DX*DX;
	PXY'	←	PXY  -  AREA*DX*DY;

ROTATION OF LAMINA INERTIA TENSOR ABOUT CENTER OF MASS.

	C	←	COSINE(PHI);
	S	←	SINE(PHI);
	MXX'	←	C*C*MXX  +  S*S*MYY  -  2*C*S*PXY;
	MYY'	←	C*C*MYY  +  S*S*MXX  +  2*C*S*PXY;
	PXY'	←	(C*C - S*S)*PXY + C*S*(MYY - MXX);


~I1973,800;F8- 51 -