Oliver Sheridan-Methven | PDF - Charterhouse

Oliver Sheridan-Methven Chaos Supervisor - DL
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Figure18
Computer Simulation by [5]
Experimental Results
So upon comparison of the
experimental results to the computer
simulation (Figure18) it is evident that the
simulations can demonstrate many of the
aspects of that occur in reality within the
system. However, it would be difficult
(almost impossible) to determine, from
the four simple equations which govern
the torque and the angular acceleration,
the nature of the phase space
trajectories and the strange attractors
present. Secondly, it has proved to be a
high quality manifestation of the logistics
map and its qualities of birefringence and
isolated regions of stability (1.31Hz) in such
a relatively simply governed system
(T1,T2,T3).
Ultimately, this experiment
demonstrates the capabilities that
strange attractors have: that a plot in
phase space can reduce the system's
apparent randomness and
unpredictability into order and patterns. From these patterns predictability can be
induced which is the ultimate aim in experimental science; combining microscopic
equations into macroscopic predictions, and the knowledge of what will happen next [2].
Throughout the history of physics and natural philosophy though, there has
always been one topic that used to take precedence over all others. During the days
when religion and science were intermingled, the stars and planets were of divine
significance. The movement of the heavenly spheres (planets) and the study of
astronomy were the professions of the educated few (natural philosophers,
mathematicians and some members of the church). Beginning with the theory of a
geocentric universe, this was changed by Nicolaus Copernicus, proposing the
heliocentric model for calculations in his book, On the Revolution of Celestial Spheres.
Following this Galileo Galilei more fully supported this idea until Johannes Kepler
published in Harmony of the World the collected data which supported, to the point of
proof, the heliocentric model. Finally the issue appeared to be settled definitively in Isaac
Newton's Mathematical Principles of Natural Philosophy. This had proved to be the most
problematic issue: predicting where the divine bodies will appear at a given time [4].
The key to Newton's success in resolving the issue definitively was to take
Galileo's concept of inertia and extend upon it with mathematical description. These are
known as Newton's three laws of motion which describe how things move. The first two
laws can be described just by the second law; that when a force acts on a body its
velocity will change. This is mathematically described by:
F = dPdt -1 =ma
The third law says for every impulse (F◦t) there is an equal and oppositely
directed impulse. This law was not crucial though in his solution for a heliocentric model.
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