Lagrange Multipliers and the Design of Multistage Rockets (UMAP)

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 ROCKETS

2. SINGLE-STAGE ROCKETS

3. OPTIMIZATION IN MULTISTAGE ROCKET DESIGN

4. REFERENCES FOR FURTHER READING

5. SOLUTIONS TO EXERCISES