Gyroscope

Index

Introduction …………………………………………………………2

Experiments ………………………………………………………...2
Numerical integration…………...…...………………………3
Analytical approach…………………………………………..6

3. Conclusions ................................................................................…..10





























1.Introduction

The gyroscope, as it is known nowadays, was invented in 1852 by the French experimental physicist León Foucault (1819-1868) as part of an investigation of the rotation of the Earth, although somepeople have had already used similar instruments before him. This instrument is a rapidly rotating disk with a heavy rim, mounted in low-friction gimbals. It tends to maintain fixed its principalaxis orientation in space thanks to the conservation of angular momentum and the absence of external torque. But this axis can also move itself, defining two types of movements: precession and nutation,which will be explained later.
This report is going to show some of the possible motions of the gyroscope, which arise due to some given values of angular velocities and angles.
For doing this wehave used the programming program “Matlab”, creating a script and a function.

2. Experiments

Firstly, in this part it is explained the two different motions of the axis of the rotating disk(precession and nutation), so that a better explanation of the motions of the gyroscope is given later.

A gyro consists on a disk that is rotating upon itself (spinning). This rotation defines animaginary line called rotation axis (body axis in figure 1.1).
Precession is a change in the orientation of the rotational axis of a rotating body. In a pure precession movement the second Euler angle(nutation) is constant.
Nutation is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object. A pure nutation is a movement of a...