MatrixEquations - HOW TO PUT A LINEAR SYSTEM OF EQUATIONS...

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HOW TO PUT A LINEAR SYSTEM OF EQUATIONS INTO MATRIX FORM The door optimization problem requires formulation of constraint equations that are linear in the unknown reaction forces and torques 1 x F , 1 y F , 1 z T , 2 x F , 2 y F , and 2 z T . Those constraint equations are derived from rigid body statics and are summarized below: Sum forces in x direction: 12 0 xx FF += Sum forces in y direction: 0 yy FFm g +−= Sum moments in z direction about point 1: 21 2 /2 0 xz z mgc F d T T ++ + = Notice that 1 x F , 1 y F , 1 z T , 2 x F , 2 y F , and 2 z T appear linearly in these three equations. For a Matlab optimization function to use these constraint equations, we need to put them into matrix form. Below is the series of steps that must be followed to achieve this goal: 1) Define a vector x containing the unknown quantities to be found. In this case, x will contain the unknown reaction loads 1 x F , 1 y F , 1 z T , 2 x F , 2 y F , and 2 z T stored in a column vector: 1 1 1 2 2 2 x y z x y z F F T x F F T ⎡⎤ ⎢⎥ = ⎣⎦ 2)
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This note was uploaded on 09/05/2011 for the course EGM 3344 taught by Professor Raphaelhaftka during the Spring '09 term at University of Florida.

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MatrixEquations - HOW TO PUT A LINEAR SYSTEM OF EQUATIONS...

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