pg_utils.sympy_supp.vector_calculus_3d.SphericalCoordinates

class pg_utils.sympy_supp.vector_calculus_3d.SphericalCoordinates(r, t, p, r_name='r', t_name='t', p_name='p')

Bases: OrthogonalCoordinates3D

Spherical coordinate system in 3D

Example: define a spherical coordinate system. The default names for the coordinates are r (radius), t (colatitude) and p (azimuth):

>>> x1, x2, x3 = sympy.symbols("x_1 x_2 x_3")
>>> sph3d = SphericalCoordinates3D(x1, x2, x3)
>>> sph3d.r   # Invoking the radial coordinate
x_1
>>> sph3d.p   # Invoking the azimuthal coordinate
x_3

You can also pass in additional names to name the coordinates:

>>> sph3d = SphericalCoordinates3D(x1, x2, x3, r_name="x1")
>>> sph3d.x1  # Invoking the radial coordinate
x_1
>>> sph3d.p  # Invoking the azimuthal coordinate
x_3

It also supports indexing:

>>> sph3d[1]
x_2

__init__(r, t, p, r_name='r', t_name='t', p_name='p') → None

Methods

__init__(r, t, p[, r_name, t_name, p_name])
curl(vector_in, **kwargs)	Vector curl, to be implemented
div(vector_in, **kwargs)	Compute the divergence of a vector in spherical coordinates
grad(scalar_in, **kwargs)	Scalar gradient, to be implemented
laplacian(tensor_in[, rank])	Tensor Laplacian, to be implemented
surface_div(vector_in, **kwargs)	Compute the surface divergence of a 2-D vector in spherical coordinates
surface_grad(scalar_in, **kwargs)	Surface gradient, to be implemented
transform_to(v_in, new_sys[, coeffs_new])

Attributes

coords

Setter/getter interface for the coordinates, indexable

property coords

Setter/getter interface for the coordinates, indexable

curl(vector_in, **kwargs)

Vector curl, to be implemented

div(vector_in, **kwargs)

Compute the divergence of a vector in spherical coordinates

Parameters:

• vector_in (array-like) – input vector, assumed to be 3-component array, with sympy.Expr as components

• **kwargs – additional arguments passed to sympy.diff

Returns:

divergence scalar, sympy.Expr

grad(scalar_in, **kwargs)

Scalar gradient, to be implemented

laplacian(tensor_in, rank=0, **kwargs)

Tensor Laplacian, to be implemented

surface_div(vector_in, **kwargs)

Compute the surface divergence of a 2-D vector in spherical coordinates

Parameters:

• vector_in (array-like) – input vector, assumed to be 2-component array, with sympy.Expr as components. These are assumed to be colatitudal (theta) and azimuthal (phi) components of a vector field.

• **kwargs – additional arguments passed to sympy.diff

Returns:

surface divergence, sympy.Expr

surface_grad(scalar_in, **kwargs)

Surface gradient, to be implemented