User:Egm6321.f10.team1.allison

Problem 1: Derive (3) and (4) on p1-3

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$$  \displaystyle \frac{d}{dt}f(y^1(t),t)= \frac{\partial f(y^1(t),t)}{\partial s} \frac{\partial y^1}{\partial t}+ \frac{\partial f(y^1(t),t)}{\partial t} $$ (3)
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$$ \frac{d^2f}{dt^2}=f,_s(y^1,t) \frac{d^2y^1}{dt^2}+f,_{ss}\left(\frac{dy^1}{dt} \right)^2+2f,_{st} \frac{dy^1}{dt}+f,_{tt} $$     (4)
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$$ c_o(y^1,t)=-F^1[1-\overline{R}(u^2,_{ss})]-F^2u^2,_s- \frac{T}{R}+M[[1-\overline{R}(u^2,_ss)][u^1,_{tt}-\overline{R}(u^2,_{stt})]+u^2,_su^2,_{tt}] $$      (4)
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