Masters Theses


"A gyrocompass with three degrees of freedom is studied and an attempt made to solve the exact equations of motion numerically. The equations are obtained by using the Lagrange formulation of the problem. The kinetic energy and the potential energy of the system are determined from the energies of the various components. These are then substituted into Lagrange's equation to obtain the three equations of motion for the three angular coordinates. As few restrictive assumptions as possible are made during this development. From these exact equations of motion an approximate analytical solution is obtained by making several assumptions and then solving the linearised equations. As the requirement of a gyrocompass is to point North at any instant, an equilibrium configuration of the system is sought to find the inclination of the gyro axis with the horizontal in a position of steady motion. The exact equations of motion are complicated. Hence they are solved with the help of a high speed digital computer using numerical methods for solving differential equations. The methods used are the Runge-Kutta method of order 4, and the Hamming method of order 1. A comparison is made between the two methods to find which is the better for solving such a system of equations. A comparison is also made between the numerical solution to the exact equations of motion and the approximate analytical solution to check the effect of the approximations made. Graphs are plotted from the results obtained. Suggestions are made for further work"--Abstract, page ii.


Barker, Clark R.

Committee Member(s)

Keith, Harold D. (Harold Dean), 1941-
Rocke, R. D. (Richard Dale), 1938-


Mechanical and Aerospace Engineering

Degree Name

M.S. in Mechanical Engineering


University of Missouri--Rolla

Publication Date



viii, 98 pages

Note about bibliography

Includes bibliographical references (page 59).


© 1969 Subhash Govind Kelkar, All rights reserved.

Document Type

Thesis - Open Access

File Type




Subject Headings

Gyro compass
Dynamics -- Mathematical models
Lagrange equations
Runge-Kutta formulas

Thesis Number

T 2204

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