PHYS310_homework_01_solutions

PHYS310_homework_01_solutions - Homework set 1 due...

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Unformatted text preview: Homework set 1, due Wednesday, August 31, 2011, 11:30 am Following problems from Analytical Mechanics by Fowles & Cassiday 1.2 (10 points) (a) ( 29 ( 29 ( 29 ˆ ˆ ˆ ˆ ˆ 2 4 (2)(1) (1)(4) (0)(1) 6 A B C i j i j k ⋅ + = + ⋅ + + = + + = v v v ( 29 ( 29 ˆ ˆ ˆ ˆ 3 4 (3)(0) (1)(4) (1)(0) 4 A B C i j k j + ⋅ = + + ⋅ = + + = v v v (b) ( 29 2 1 1 1 8 4 A B C ⋅ × = = - v v v ( 29 ( 29 8 A B C A B C × ⋅ = ⋅ × = - v v v v v v (c) ( 29 ( 29 ( 29 ( 29 ( 29 ˆ ˆ ˆ ˆ ˆ ˆ 4 2 4 4 8 4 A B C A C B A B C i k j i j k × × = ⋅- ⋅ = +- =- + v v v v v v v v v ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ˆ ˆ ˆ ˆ ˆ ˆ 0 2 4 4 4 A B C C A B C B A C A B i j i k i k × × = - × × = - ⋅- ⋅ = - +- + = + v v v v v v v v v v v v 1.4 (10 points) (a) ˆ ˆ ˆ A i j k = + + v : body diagonal ˆ ˆ ˆ ˆ ˆ ˆ 3 A A A i i j j k k = ⋅ = ⋅ + ⋅ + ⋅ = v v (b) ˆ ˆ B i j = + v : face diagonal 2 B B B = ⋅ = v v (c) ˆ ˆ ˆ 1 1 1 1 1 i j k C A B = × = v v...
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PHYS310_homework_01_solutions - Homework set 1 due...

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