p0262 - 174 CHAPTER 2. PARTICLE KINEMATICS 2.62 Chapter 2,...

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174 CHAPTER 2. PARTICLE KINEMATICS 2.62 Chapter 2, Problem 62 Problem: Consider the vectors A = x i + x 1 j and B = x i + x 2 j . Compute the first derivative of A × B with respect to x by forming the cross product and differentiating. Verify that the chain rule for a cross product [Equation (2.38)] yields the same derivative. Solution: The cross product of A and B is A × B = e e e e e e e ijk xx 1 0 2 0 e e e e e e e = D x 3 1 i k Differentiation with respect to x yields d dx ( A × B )=3 x 2 k To check for consistency with the chain rule, note that
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This note was uploaded on 05/11/2011 for the course AME 301 taught by Professor Shiflett during the Spring '06 term at USC.

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