PHYS217 - Chaos - Solutions#2
B&G 2.6) The system of has the three functions
Fx = y x
Fy = r x y x z
Fz = x y b z
associated with each derivative. A conservative system has F =
Fx
x
+
Fy
y
+
Fz
z
= 0. In this case,
F = + 1 + b
This is not zero for positi
PHYS217 - Chaos - Solutions #4
PHYS217-1) a) With careful study of the phase plots of the "pendulum.exe" solutions, one is just able to
get the bifurcation points to five digits. This would be much easier if the scale could be expanded about an
arbitrary
PHYS217 - Chaos - Solutions#3
PHYS217-1) a) Here is the Mathcad version. The Excel spreadsheet will be very similar to last week's
Lorentz system, with different functions.
(1) Starting at , , and , take a test half Euler step.
h
h = h +
h
sin ( ) +
PHYS 217 - Chaos - Quiz #2 - 11/15/10 Name_
1) What are the fixed points of the undriven, damped pendulum system,
d
= ,
d
= sin( )
? Sketch a
dt
dt
q
trajectory near any one of the fixed points stating clearly which fixed point is associated with your sk
PHYS 217 - Chaos - Quiz #3 - 12/01/10 Name_
1) Our working definition of a chaotic system has evolved into: "(1) deterministic; (2) aperiodic; (3) positive Lyapunov
exponent" Supply a short sentence expanding the meaning of each point.
Answer) 1) The futu
PHYS 217 - Chaos - Quiz #1 - 11/03/10 Name_
1) a) Write down any second order, linear differential equation. b) Write down any nonlinear function of x and y. c) Write
down any set of two coupled, first order, nonlinear differential equations.
Answer) a) S
PHYS 217 Chaos
Solutions #1
PHYS217-1) I have posted my Excel spreadsheet on the web-page with both the Euler, and midpoint Euler
methods illustrated. Here, I show how the same calculations - and more - can be done in Mathcad, the
software with which I wr
PHYS 217 - Chaos - Quiz #4 - 12/10/10 Name_
1) What is the fractal dimension of the set of points represented on the back of this sheet? Assume that the pattern
continues up and down to all magnifications.
d
Answer) The fractal dimension is the power that