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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 -