pg_utils.sympy_supp.vector_calculus_3d.OrthogonalCoordinates3D

class pg_utils.sympy_supp.vector_calculus_3d.OrthogonalCoordinates3D(x1, x2, x3, x1_name=None, x2_name=None, x3_name=None)[source]

Bases: object

Base class for orthogonal curvilinear coordinates in 3D

Example: define a Cartesian system:

x, y, z = sympy.symbols("x y z")
cart3d = OrthogonalCoordinates3D(x, y, z, x1_name='x', x2_name='y', x3_name='z')

OrthogonalCoordinates3D implements indexing. The coordinates can be retrieved in two different ways (following last example):

>>> cart3d.y    # invoking coordinate by name
y
>>> cart3d[1]   # invoking coordinate by index
y

Computational utilities of OrthogonalCoordinates3D, such as grad, curl etc., are all abstract methods; therefore, the class is intended to be inherited and used, instead of being used directly.

__init__(x1, x2, x3, x1_name=None, x2_name=None, x3_name=None) → None[source]

Constructor

Parameters:

x1 (sympy.Symbol) – first coordinate
x2 (sympy.Symbol) – second coordinate
x3 (sympy.Symbol) – third coordinate
x1_name (str) – optional name for x1; if given, the attribute will be named by x1_name; else, the attribute will be named “x1”.
x2_name (str) – see x1_name
x3_name (str) – see x1_name

Methods

`__init__`(x1, x2, x3[, x1_name, x2_name, x3_name])	Constructor
`curl`(vector_in, **kwargs)	Compute curl/rot of a vector
`div`(vector_in, **kwargs)	Compute divergence of a vector
`grad`(scalar_in, **kwargs)	Compute gradient of a scalar
`laplacian`(tensor_in[, rank])	Compute Laplacian of a tensor
`transform_to`(tensor_in, new_sys[, coeffs_new])	Transform to other coordinate systems

Attributes

coords

Setter/getter interface for the coordinates, indexable

property coords[source]: Setter/getter interface for the coordinates, indexable

curl(vector_in, **kwargs)[source]

Compute curl/rot of a vector