pg_utils.sympy_supp.vector_calculus_3d.CylindricalCoordinates

class pg_utils.sympy_supp.vector_calculus_3d.CylindricalCoordinates(s, p, z, s_name='s', p_name='p', z_name='z')

Bases: OrthogonalCoordinates3D

Cylindrical coordinate system in 3D

Example: define a cylindrical system. The default names for the coordinates are s, p and z:

>>> x1, x2, x3 = sympy.symbols("x_1 x_2 x_3")
>>> cyl3d = CylindricalCoordinates3D(x1, x2, x3)
>>> cyl3d.s   # Invoking the radial coordinate
x_1
>>> cyl3d.p   # Invoking the azimuthal coordinate
x_2

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

>>> cyl3d = CylindricalCoordinates3D(x1, x2, x3, s_name="r")
>>> cyl3d.r  # Invoking the radial coordinate
x_1
>>> cyl3d.p  # Invoking the azimuthal coordinate
x_2

It also supports indexing:

>>> cyl3d[2]
x_3

__init__(s, p, z, s_name='s', p_name='p', z_name='z') → None

Constructor

Parameters:

• s (sympy.Symbol) – radial coordinate

• p (sympy.Symbol) – azimuthal coordinate

• z (sympy.Symbol) – vertical coordinate

• s_name (str) – optional name for s; if given, the attribute will be named by s_name; else, the attribute will be named “s”.

• p_name (str) – see s_name

• z_name (str) – see s_name

Methods

__init__(s, p, z[, s_name, p_name, z_name])	Constructor
curl(vector_in, **kwargs)	Compute the curl of a vector in cylindrical coordinates
div(vector_in, **kwargs)	Compute the divergence of a vector in cylindrical coordinates
grad(scalar_in, **kwargs)	Compute the grad of a scalar in cylindrical coordinates
laplacian(tensor_in[, rank])	Compute the Laplacian of a tensor in cylindrical coordinates
transform_to(v_in, new_sys[, coeffs_new])	Transform vector under cylindrical coordinates to new coordinate system

Attributes

coords

Setter/getter interface for the coordinates, indexable

property coords

Setter/getter interface for the coordinates, indexable

curl(vector_in, **kwargs)

Compute the curl of a vector in cylindrical 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:

curl, 3-tuple of sympy.Expr, with elements corresponding to (s,p,z) components

div(vector_in, **kwargs)

Compute the divergence of a vector in cylindrical 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)

Compute the grad of a scalar in cylindrical coordinates

Parameters:

• scalar_in (sympy.Expr) – input scalar

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

Returns:

gradient, 3-tuple of sympy.Expr, with elements corresponding to (s,p,z) components

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

Compute the Laplacian of a tensor in cylindrical coordinates

Parameters:

• tensor_in – input tensor

• rank (int) – rank of the input tensor, default to 0. Currently, only rank = 0 (scalar Laplacian) is implemented.

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

Returns:

tensor, sympy.Expr or List of sympy.Expr depending on the input tensor rank

transform_to(v_in: Vector3D, new_sys: OrthogonalCoordinates3D, coeffs_new=False) → Vector3D

Transform vector under cylindrical coordinates to new coordinate system