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VectorCalculus

  

MapToBasis

  

convert Vectors and vector fields between different coordinate systems

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

MapToBasis(V,c,p)

Parameters

V

-

Vector(algebraic) or Vector valued procedure; specify the free Vector, rooted Vector of vector field to be converted

c

-

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

p

-

(optional) list or Vector(algebraic); specify the target root point.

Description

• 

The MapToBasis(V, c) command converts Vectors and vector fields between different coordinate systems.

• 

If V is a Vector valued procedure, it is interpreted as a vector field. Otherwise, a vector field is a Vector created by a call to the VectorField routine.

• 

If c is not specified, the current coordinate system is used. If V represents a vector field, the implied coordinates 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. Otherwise, the object is interpreted as a Vector or vector field in the current coordinate system. If the two are not compatible, an error is raised.

• 

If p is specified and v is a free Vector in Cartesian coordinates, the result will be a rooted Vector with a root point p. If p is a list, it will be interpreted as Cartesian coordinates.

Examples

withVectorCalculus:

MapToBasis with free Vectors

GetCoordinates

cartesian

(1)

v1MapToBasis1,1,polar

v1:=2er+14πeθ

(2)

MapToBasisv1,cartesian

ex+ey

(3)

v2r,θ

v2:=rex+θey

(4)

SetCoordinatesv2,polar

rer+θeθ

(5)

MapToBasisv2

rcosθex+rsinθey

(6)

Using MapToBasis with free Vectors to get a rooted Vector

v3MapToBasisa,b,polar,0,1

v3:=ba

(7)

Aboutv3

Type: Rooted VectorComponents: b,aCoordinates: polarRoot Point: 1,12π

(8)

SetCoordinatessphericalr,φ,θ

sphericalr,φ,θ

(9)

MapToBasis with vector fields

VFVectorFieldr,0,0

VF:=re_r

(10)

MapToBasisVF,cartesianx,y,z

xe_x+ye_y+ze_z

(11)

MapToBasis with Vector-valued procedures

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

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

(12)

See Also

VectorCalculus

VectorCalculus[Coordinates]

VectorCalculus[GetCoordinates]

VectorCalculus[PositionVector]

VectorCalculus[RootedVector]

VectorCalculus[SetCoordinates]

VectorCalculus[Vector]

VectorCalculus[VectorField]

 


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