GIF Animations of
Phase Space Topography, of Nonlinear Dynamical
Systems,
During Parameter Variation
- Linear pendulum oscillator;
Hamiltonian is H(x,y,a)=(1/2)y2
-a.Sin[x(Pi/2)].
Parameter "a" is varied from to 0.5 to 4.0
- Bi-parabolic oscillator;
Hamiltonian is H(x,y,a)=(1/3)y3-y
-a.[x-(1/3)x3].
Parameter "a" is varied from 0.5 to 3.125.
- Quadratic pendulum oscillator;
Hamiltonian is H(x,y,a)=(1/3)y3-y
-a.Sin[x(Pi/2)].
Parameter "a" is varied from to 0.3 to 2.0
and then from 2 to 4.
- Cubic pendulum oscillator;
Hamiltonian is H(x,y,a,b)=(1/2)y2-b2(1/4)y4
-a.Sin[x(Pi/2)].
Parameter "b" is varied from 0.1 to 1
with some dwelling on the range b=[0.3,0.4]; parameter "a" held fixed at a=1.
- Cubic pendulum oscillator;
Hamiltonian as above.
Parameter "b" is varied from to 0.8 to 0.14
while parameter "a" varies as a=1/(8.b2).
- Quartic pendulum oscillator;
Hamiltonian is H(x,y,a)=(1/3)y3-y-b2(1/5)y5
-a.Sin[x(Pi/2)].
Parameter "b" held fixed at b=1/3 while
"a" is varied from 0.1 to 0.9 and then (varying more quickly) from
0.9 to 2.9.
- Quartic pendulum oscillator;
Hamiltonian as above.
Parameter "a" held fixed at a=3/4 while
"b" is varied from 0.1 to 0.5.
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