1. Chaos ~ another limit of classical theory
Near points of instability the expected predictability of classical
law can break down. This happens because of our necessarily
incomplete knowledge of initial conditions.
The new feature is that almost identical initial conditions lead to completely
different outcomes.
Example: pencil stands on sharp point
: metal near non-uniform magnetic field

6. Chaos

8. Poincare Plots

16. Brownian motion – an example of fractal paths
Over a vast range of time steps Brownian motion is fractal so that a precise velocity
cannot be assigned.
If we call the path length L and the step size x then they are related via a power law:
L = const. * x(1-D)
where D is the ‘fractal dimension’ of the path
A normal, smooth curve has L independent of x, or D = 1.
For Brownian paths one finds D = 2.
As we make x smaller, L increases. The molecular collison time (mean free path time)
sets a limit.

17. Attractors

20. Magnetic brakes

21. Gravitational Torsional Balance - Cavendish Experiment
weighing the earth
A principal discussion of the torsion
pendulum following two methods.
Manual procedures differ a little.

22. What we measure:

24. so neglect (d/w)2
Is max at b = 51.6 degree so b’ =0 and

27. Corrections:
Issue other masses nearby
Periods T1, T2 show fluctuations ~ 1ms
Issue time fluctuations

28. Issue sphericity
For accurate results DT should be as large as possible