Conventions and Notation¶
To maintain consistency, the following conventions are used throughout the library
Frames of reference¶
In general, the magnets are implemented in their own, rotated frame of reference (referred to by dashes throughout). When each magnet instance is generated, this frame is defined by two angles, theta and phi. Both are given in degrees.
Rotations are all right-handed, i.e. a positive angle rotation around an axis results in a counter-clockwise movement, when viewed from positive-infinity on that axis
Theta¶
theta is the azimuthal angle, i.e. rotation around the global Z axis. If phi=0°, then the X'-Y' plane is in the same plane as the X-Y frame, but rotated around the Z=Z' axis.
Phi¶
phi is the polar angle, i.e. the rotation around the global X axis. If theta=0°, then the Y'-Z' plane is in the same plane as the Y-Z frame, but rotated around the X=X' axis.
Order¶
Due to the use of extrinsic angles, the order of operations is important. When a frame is specified with both theta != 0, phi != 0, the frame is first rotated around the X axis by angle phi, and second rotated around the Z axis by angle theta
Note¶
Rotation around the global Y axis is not currently supported.
All rotations are spherical, i.e. around the origin (0, 0, 0) in the global frame. Consequently, this package does not (currently) support completely arbitrary magnets, as the experiment it was written to support did not require that degree of complexity.
Principal Axes¶
By convention, all magnets are defined with respect to the Y' axis
* Rectangular permanent magnets have their magnetisation pointing along the Y' axis
* Electromagnetic coils have their windings parallel to the X'-Z' plane, wrapped around the Y' axis
Units¶
SI units are used throughout - metres, Tesla, Amps, etc.
Rectilinear magnets are always specifed by their full length.
Circular magnets are always specifed by their radius
Handling groups of magnets¶
As a general rule, methods which operate on a magnet will accept either a single magnet, or an iterable (list, tuple etc) containing multiple magnets.