154 allocation of interdiction eort a smuggler moves

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Unformatted text preview: derive equations that relate these quantities via energy balance: 12 1 msi+1 + mghi+1 = ms2 + mghi + ηfi − dCD s2 , i 2 2i i = 1, . . . , N, where g = 9.8 is the gravitational acceleration. The lefthand side is the total vehicle energy (kinetic plus potential) after it passes through knot point pi+1 ; the righthand side is the total vehicle energy after it passes through knot point pi , plus the energy gain from the fuel burn, minus the energy lost to drag. To set up the first vehicle speed s1 requires an additional initial fuel burn f0 , with 1 ηf0 = 2 ms2 . 1 Fuel is also used to power the on-board system of the vehicle. The total fuel used for this purpose is fob , where ηfob = T P , where P > 0 is the (constant) power consumption of the on-board system. We have a fuel capacity constraint: N fi + fob ≤ F , where F > 0 is the total initial fuel. i=0 The problem data are m, d, h1 , . . . , hN +1 , η , CD , P , and F . (You don’t need the knot points pi .) (a) Explain ho...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.

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