# Lagrange Multipliers and the Design of Multistage Rockets (UMAP)

### Author: Anthony Peressini

A unit that uses Lagrange multipliers to compute the minimum total mass of an n-stage rocket capable of placing a given payload in an orbit at a given altitude above the earth's surface. Upon completion of this module students will be able to understand: 1) the derivation of the rocket equation; 2) the computation of the velocity increment provided; 3) how Lagrange multipliers show that three-stage rockets are the best practical choice among multistage rockets for earth-orbit missions.** Table of Contents:1. SOME BASIC DESIGN QUESTIONS FOR MULTISTAGE ROCKETS2. SINGLE-STAGE ROCKETS3. OPTIMIZATION IN MULTISTAGE ROCKET DESIGN4. REFERENCES FOR FURTHER READING5. SOLUTIONS TO EXERCISES**

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