Analytical Mech Homework Solutions 85

Analytical Mech Homework Solutions 85 - Chapter 7 Dynamics...

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Chapter 7 Dynamics of Systems of Particles z 7.1 From eqn. 7.1.1, 1 cm i i i rm m = r GG 3 2 1 y x () 123 11 ˆˆ ˆˆˆ 33 cm rr r ri j j k = + + = ++++ G G k 1 ˆ 22 3 cm j =++ G k ( ) ˆ ˆˆˆˆ 2 cm cm d vrv v v i j i j dt ==+ + =+ + + + GGG G G k 1 ˆ 32 3 cm vi j + G k 3 From eqn 7.1.3, 12 ii i p mv v v v == + G G + G ˆ p ij G k 7.2 (a) From eqn. 7.2.15, 2 1 2 i = Tm v 22 222 1 21 111 4 2 T  + + + =  (b) From Prob. 7.1, 1 ˆ 3 cm j + G k 2 2 1 2 9 cm mv =×× G 1 3 v (c) From eqn.7.2.8, i Lr m () () ( ) ˆ ˆ ˆ 2 Li ji j k jk i j k =+×++×+×+ + G G ˆ 2 k omentum i ()()( ) ˆ ˆ ˆ Lki j j =− +− + − =− + − 7.3 bg vvv D Since m
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