bv_cvxbook_extra_exercises

154 allocation of interdiction eort a smuggler moves

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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.

Ask a homework question - tutors are online