List of Examples

Contents

• 1 Magnetic Fields on the 2-Torus
• 2 Other Fields
• 3 2nd Order Autonomous ODEs

Magnetic Fields on the 2-Torus

The following examples represent magnetic fields on the 2-torus. All of the following examples have u = cos(2 * PI * z) and v = sin(2 * PI * z).

Example 1	w = 0	This is the most basic case.
Example 2	w = c	Constant w component.
Example 3	w = c * cos(2 * PI * x)
Example 4	w = sin(2 * PI * x) + cos(2 * PI * y)

Other Fields

The following examples are not constrained to u = cos(2 * PI * z) and v = sin(2 * PI * z).

Example 5

u = 2 * sin(2 * PI * z), v = sin(2 * PI * y) + 2 * cos (2 * PI * z), w = cos(2 * PI * x)

2nd Order Autonomous ODEs

The following examples use 2nd order autonomous ODEs.

Example 6

a = sin(4*PI*(x-y)) / (2*(cos(2*PI*(x-y))-2)) * v_x*v_x - sin(2*PI*(x-y)) / (2-cos(2*PI*(x-y))) * v_y*v_y, b = -2*sin(2*PI*(x-y)) / (2-cos(2*PI*(x-y))) * v_x*v_x - sin(4*PI*(x-y)) / (2*(cos(2*PI*(x-y))-2)) * v_y*v_y

Double Pendulum