Plot[- .5 x ^ 2 + .25 x ^ 4, {x, - 2, 2}]
2.0
1.5
1.0
0.5
-2
1
-1
2
c=2
2
A = Plot[ {Sqrt[c + x ^ 2 - 0.5 x ^ 4], - Sqrt[c + x ^ 2 - 0.5 x ^ 4]}, {x, - 2, 2}]
1.5
1.0
0.5
-2
1
-1
-0.5
-1.0
-1.5
c=1
1
2
2
Mathematica level curves of Double Well+Pendulum.nb
B = Plot[ {Sqrt[c + x ^ 2 - 0.5 x ^ 4], - Sqrt[c + x ^ 2 - 0.5 x ^ 4]}, {x, - 2, 2}]
1.0
0.5
-2
1
-1
2
-0.5
-1.0
c = .1
0.1
CC = Plot[ {Sqrt[c + x ^ 2 - 0.5 x ^ 4], - Sqrt[c + x ^ 2 - 0.5 x ^ 4]}, {x, - 2, 2}]
0.5
-2
1
-1
-0.5
c = .01
0.01
2
Mathematica level curves of Double Well+Pendulum.nb
DD = Plot[ {Sqrt[c + x ^ 2 - 0.5 x ^ 4], - Sqrt[c + x ^ 2 - 0.5 x ^ 4]}, {x, - 2, 2}]
0.6
0.4
0.2
-2
1
-1
2
-0.2
-0.4
-0.6
c = 0; Plot[ {Sqrt[c + x ^ 2 - 0.5 x ^ 4], - Sqrt[c + x ^ 2 - 0.5 x ^ 4]}, {x, - 2, 2}]
0.6
0.4
0.2
-2
1
-1
2
-0.2
-0.4
-0.6
c = - .1
- 0.1
EE = Plot[ {Sqrt[c + x ^ 2 - 0.5 x ^ 4], - Sqrt[c + x ^ 2 - 0.5 x ^ 4]}, {x, - 2, 2}]
0.6
0.4
0.2
-2
1
-1
-0.2
-0.4
-0.6
2
3
4
Mathematica level curves of Double Well+Pendulum.nb
c = - 0.2
- 0.2
F = Plot[ {Sqrt[c + x ^ 2 - 0.5 x ^ 4], - Sqrt[c + x ^ 2 - 0.5 x ^ 4]}, {x, - 2, 2}]
0.6
0.4
0.2
-2
1
-1
2
-0.2
-0.4
-0.6
c = - 0.45
- 0.45
G = Plot[ {Sqrt[c + x ^ 2 - 0.5 x ^ 4], - Sqrt[c + x ^ 2 - 0.5 x ^ 4]}, {x, - 2, 2}]
0.2
0.1
-2
1
-1
-0.1
-0.2
2
Mathematica level curves of Double Well+Pendulum.nb
Show[A, B, CC, DD, EE, F, G]
1.5
1.0
0.5
-2
1
-1
2
-0.5
-1.0
-1.5
c = - 1.1
- 1.1
Plot[ {Sqrt[2 (c + Cos[x])], - Sqrt[2 (c + Cos[x])]}, {x, - 6, 6}]
1.0
0.8
0.6
0.4
0.2
-6
c = -1
-1
-4
-2
2
4
6
5
6
Mathematica level curves of Double Well+Pendulum.nb
Plot[ {Sqrt[2 (c + Cos[x])], - Sqrt[2 (c + Cos[x])]}, {x, - 6, 6}]
1.0
0.8
0.6
0.4
0.2
-6
-4
2
-2
4
6
c = - .5
- 0.5
Plot[ {Sqrt[2 (c + Cos[x])], - Sqrt[2 (c + Cos[x])]}, {x, - 6, 6}]
1.0
0.5
-6
-4
2
-2
-0.5
-1.0
c=0
0
4
6
Mathematica level curves of Double Well+Pendulum.nb
Plot[ {Sqrt[2 (c + Cos[x])], - Sqrt[2 (c + Cos[x])]}, {x, - 6, 6}]
1.5
1.0
0.5
-6
-4
2
-2
4
6
-0.5
-1.0
-1.5
c=1
1
Plot[ {Sqrt[2 (c + Cos[x])], - Sqrt[2 (c + Cos[x])]}, {x, - 6, 6}]
2
1
-6
-4
2
-2
-1
-2
c = 1.1
1.1
4
6
7
8
Mathematica level curves of Double Well+Pendulum.nb
Plot[ {Sqrt[2 (c + Cos[x])], - Sqrt[2 (c + Cos[x])]}, {x, - 6, 6}]
2
1
-6
-4
2
-2
4
6
-1
-2
c=3
3
Plot[ {Sqrt[2 (c + Cos[x])], - Sqrt[2 (c + Cos[x])]}, {x, - 6, 6}]
3
2
1
-6
-4
2
-2
-1
-2
-3
4
6
Mathematica level curves of Double Well+Pendulum.nb
ContourPlotv ^ 2  2 + x ^ 4  4 - x ^ 2  2,
{x, - 1.1, - .9}, {v, - .1, .1}, ContourShading → None
0.10
0.05
0.00
-0.05
-0.10
-1.10
-1.05
-1.00
-0.95
-0.90
ContourPlotv ^ 2  2 + x ^ 4  4 - x ^ 2  2, {x, - 2, 2}, {v, - 2, 2}, ContourShading → None
2
1
0
-1
-2
-2
-1
0
1
2
9
10
Mathematica level curves of Double Well+Pendulum.nb
ContourPlotv ^ 2  2 + x ^ 4  4 - x ^ 2  2,
{x, - 1.1, - .9}, {v, - .1, .1}, ContourShading → None
0.10
0.05
0.00
-0.05
-0.10
-1.10
-1.05
-1.00
-0.95
-0.90