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Analytical Mech Homework Solutions 3

Analytical Mech Homework Solutions 3 - 0 = A B = q q 3 q(1...

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1.7 ( )( ) ( )( ) ( )( ) 2 1 2 A B q q q q q = = + + = + K K 0 3 3 2 0 ( ) , q ( ) 2 1 q q = 1 = or 2 1.8 ( ) ( ) 2 2 2 2 A B A B A B A B + = + + = + + K K K K K K A B K K 2 2 2 2 A B A B AB + = + + K K Since , cos A B AB AB θ = K K A B A B + + K K K K K K cos cos A B AB A B A B θ θ = = K K K K cos B B θ 1.9 Show ( ) ( ) ( ) C A C B A B C × × = K K K K K K K A B K K or ( ) ( ˆ ˆ ˆ x y z x x y y z z x x y y z z x y z i j k B B A C A C A C B A B A B A B C C C C × = + + + + K K K ( ) ˆ x x y x y z x z x x x y y x z z x C A B C A B C A B C A B C A B C i = + + ( ) ˆ x y y y z y z x x y y y y z z y C A B C A B C A B C A B C A B C j + + + ( ) ˆ x y z y z z z x x z y y z z z z C A B C A B C A B C A B C A B C k + + + ) A B x A B x y A B
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