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VectorCalculus

  

*

  

An overloaded version of Star that deals with scalar multiplication of Vectors

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

s*v

Parameters

s

-

algebraic; the scalar to scale the Vector

v

-

Vector(algebraic); the Vector to scale

Description

• 

Returns the scalar multiplication of s and v.

• 

An overloaded version for the VectorCalculus package that deals with scaling Vectors (scalar multiplication) in different coordinate systems.

• 

The following table describes the interaction between different types of Vector objects in different coordinate systems when the Star operator is applied.

 

v

coord(v)

s*v

coord(s*v)

1

free Vector

cartesian

free Vector

cartesian

 

free Vector

curved

error

 

2

rooted Vector(root)

any

rooted Vector (root)

any

3

vector field

any

vector field

any

4

position Vector

cartesian

position Vector

cartesian

• 

Note that in 2-D math, the Star operator appears as a dot.

Examples

withVectorCalculus:

Only free Vectors in cartesian coordinates can be scaled.

21,1,2

2ex+2ey+4ez

(1)

v1Vector1,2,coordinates=cartesianx,y

v1:=ex+2ey

(2)

3v1

3ex+6ey

(3)

Rooted Vectors in any coordinate system can be scaled.

v2RootedVectorroot=1,π2,1,2,polarr,t

v2:=12

(4)

3v2

36

(5)

v3RootedVectorroot=1,2,1,1,parabolicu,v

v3:=11

(6)

2v3

22

(7)

Vector Fields in any coordinate system can be scaled.

vfVectorFieldx,y,cartesianx,y

vf:=xe_x+ye_y

(8)

xvf

x2e_x+xye_y

(9)

Position Vectors can be scaled.

pvPositionVectorp,p,polarr,t

pv:=pcosppsinp

(10)

1pv2

12pcosp12psinp

(11)

See Also

VectorCalculus

VectorCalculus[PositionVector]

VectorCalculus[RootedVector]

VectorCalculus[Vector]

VectorCalculus[VectorField]

 


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