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VectorCalculus

  

PositionVector

  

create a position Vector with specified components and a coordinate system

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

PositionVector(comps)

PositionVector(comps, c)

Parameters

comps

-

list(algebraic); specify the components of the position Vector

c

-

symbol or symbol[name, name, ...]; specify the coordinate system, possibly indexed by the coordinate names

Description

• 

The PositionVector procedure constructs a position Vector, one of the principal data structures of the Vector Calculus package.

• 

The call PositionVector(comps, c) returns a position Vector in a Cartesian enveloping space with components interpreted using the corresponding transformations from c coordinates to Cartesian coordinates.

• 

If no coordinate system argument is present, the components of the position Vector are interpreted in the current coordinate system (see SetCoordinates).

• 

The position Vector is a Cartesian Vector rooted at the origin, and has no mathematical meaning in non-Cartesian coordinates.

• 

The c parameter specifies the coordinate system in which the components are interpreted; they will be transformed into Cartesian coordinates.

• 

For more information about coordinate systems supported by VectorCalculus, see VectorCalculus,Coordinates.

• 

If comps has indeterminates representing parameters, the position Vector serves to represent a curve or a surface.

– 

To differentiate a curve or a surface specified via a position Vector, use diff.

– 

To evaluate a curve or a surface given by a position Vector, use eval.

– 

To evaluate a vector field along a curve or a surface given by a position Vector, use evalVF.

– 

A curve or surface given by a position Vector can be plotted using PlotPositionVector.

• 

The position Vector is displayed in column notation in the same manner as rooted Vectors are, as a position Vector can be interpreted as a Vector that is (always) rooted at the Cartesian origin.

• 

A position Vector cannot be mapped to a basis different than Cartesian coordinates.  In order to see how the same position Vector would be described in other coordinate systems, use GetPVDescription.

• 

Standard binary operations between position Vectors like +/-,*, Dot Product, Cross Product are defined.

• 

Binary operations between position Vectors and vector fields, free Vectors or rooted Vectors are not defined; however, a position Vector can be converted to a free Vector in Cartesian coordinates via ConvertVector.

• 

For details on the differences between position Vectors, rooted Vectors and free Vectors, see VectorCalculus,Details.

Examples

withVectorCalculus:

Position Vectors

pv1PositionVector1,2,3,cartesianx,y,z

pv1:=123

(1)

Aboutpv1

Type: Position VectorComponents: 1,2,3Coordinates: cartesianx,y,zRoot Point: 0,0,0

(2)

PositionVector1,π2,polarr,t

01

(3)

PositionVector1,3,parabolicu,v

43

(4)

Curves

R1PositionVectorp,p2,cartesianx,y

R1:=pp2

(5)

PlotPositionVectorR1,p=1..2

R2PositionVectorv,v,polarr,θ

R2:=vcosvvsinv

(6)

PlotPositionVectorR2,v=0..3π

R3PositionVector1,π2+arctan1t2,t,spherical

R3:=2costt2+42sintt2+4tt2+4

(7)

PlotPositionVectorR3,t=0..4π

Surfaces

S1PositionVectort,v1+t2,vt1+t2,cartesianx,y,z

S1:=tvt2+1vtt2+1

(8)

PlotPositionVectorS1,t=3..3,v=3..3

S2PositionVector1,p,q,toroidalr,p,t

S2:=sinhpcosqcoshpcos1sinhpsinqcoshpcos1sin1coshpcos1

(9)

PlotPositionVectorS2,p=0..2π,q=0..2π

See Also

VectorCalculus

VectorCalculus[diff]

VectorCalculus[eval]

VectorCalculus[evalVF]

VectorCalculus[PlotPositionVector]

VectorCalculus[RootedVector]

 


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