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Student[VectorCalculus]

  

MapToBasis

  

convert a Vector or vector field to a different coordinate system

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

MapToBasis(V, c)

Parameters

V

-

Vector or Vector-valued procedure; specify the Vector or vector field

c

-

(optional) name or name[name, name, ...]; specify the new coordinate system

Description

• 

The MapToBasis(V, c) calling sequence converts the Vector or vector field V to the coordinate system c.

• 

If V is a Vector-valued procedure, it is interpreted as a vector field.

• 

If c is not specified, the current default coordinate system is used as the new coordinate system.

  

If c is specified and V represents a vector field, the new coordinate system must be indexed with the names of the new coordinates.  Otherwise, an error is raised.  If V represents a Vector, no coordinate names are required.

• 

If a coordinate system attribute is specified on V, V is interpreted in this coordinate system.

  

If a coordinate system attribute is not specified on V, V is interpreted as a Vector or vector field in the current default coordinate system.  If the default coordinate system is not compatible with the new coordinate system, an error is raised.

Examples

withStudent[VectorCalculus]:

GetCoordinates

cartesian

(1)

MapToBasis1,1,'polar'

2er+14πeθ

(2)

MapToBasis,'cartesian'

ex+ey

(3)

vr,θ

v:=rex+θey

(4)

SetCoordinatesv,'polar'

rer+θeθ

(5)

MapToBasisv

rcosθex+rsinθey

(6)

When transforming vector fields, you must specify coordinate names for the new coordinate system.

SetCoordinatessphericalr,φ,θ

sphericalr,φ,θ

(7)

vVectorFieldr,0,0

v:=re_r

(8)

MapToBasisv,cartesianx,y,z

xe_x+ye_y+ze_z

(9)

MapToBasisr,φ,θ→1r2,0,0,cartesianx,y,z

xx2+y2+z23/2e_x+yx2+y2+z23/2e_y+zx2+y2+z23/2e_z

(10)

See Also

Coordinates

Student[VectorCalculus]

Student[VectorCalculus][GetCoordinates]

Student[VectorCalculus][SetCoordinates]

Student[VectorCalculus][Vector]

Student[VectorCalculus][VectorField]

 


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