Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 17EQ
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Transcribed Image Text:Problem: Minimize the total mass M = M1+ M2 + M3 of the rocket subject to the
constraint that the required velocity vs is attained.
Apply the method of Lagrange multipliers.
Find the minimum of M as a function of vs.
(1) A final velocity of 17500 mi/h is required to place a rocket into orbit 100 miles
above the earth's surface. Suppose that the structural factor S = 0.2 and the
exhaust speed is c= 6000 mi/h.
Find the minimum total mass M of the rocket as a function of A. Find the
mass of each individual stage as a function of A.
(2) A final velocity of 24700 mi/h is required to escape earth's gravity. Suppose
that the structural factor S = 0.2 and the exhaust speed is c = 6000 mi/h.
Find the mass of each individual stage that would minimize the total mass
and allow the rocket to propel a 500 pound probe into deep space.
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