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.
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 ea
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 , t
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 stati
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 e
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, firs
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
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 magnificat