Analytical Mech Homework Solutions 59

Analytical Mech Homework Solutions 59 - 1 z ( t ) = gt 2 +...

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() 22 1 sin cos cos 0 2 zt g t v t v t αω α λ ′′ =− + + = DD or 2 sin 2 sin 2c o s c o s vv t gv g ωα =≈ D We have ignored the second term in the denominator—since v D would have to be impossibly large for the value of that term to approach the magnitude g For example, for 41 45 oo and λα == o s c o s g v ω αλ ≈− or 144 gk s ≈≈ D m v ! Substituting t into equation 5.4.15b to find the lateral deflection gives [] 3 2 4 cos sin sin sin cos v yt v t g D D ± 5.18 L e t a D G = acceleration of object relative to Earth G D = ˆ k D A D = its angular speed R G 0 R G r G y x G = acceleration of satellite ˆ k = G = its angular speed ( ) 2 aa v r A ωω = +××+ G G GG G G (Equation 5.2.14) G G G G G G 2 aa A v r = −− ×−×× As in prob em 5.7 Evaluate the term G G l ( ) aA r R R RR = − −××= × × −××−×× − DDD D G G G GGG G G ( ) a R ∆= G G a … given the condition that 23 R R = 3 2 3 1
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