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VectorCalculus

  

+

  

An overloaded version of Plus that deals with adding Vectors

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

v1 + v2

Parameters

v1

-

Vector(algebraic); the first Vector to add

v2

-

Vector(algebraic); the second Vector to add

Description

• 

Returns the sum of the two Vectors.

• 

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

 

v1

coord(v1)

v2

coord(v2)

v1+v2

coord

1

free Vector

cartesian

free Vector

cartesian

free Vector

cartesian

 

free Vector

curved

free Vector

any

error

 

2

free Vector

cartesian

rooted Vector (root2)

coord2

rooted Vector (root2)

coord2

3

free Vector

any

vector field

any

error

 

4

free Vector

cartesian

position Vector

cartesian

free Vector

cartesian

 

free Vector

curved

position Vector

cartesian

error

 

5

rooted Vector (root1)

coord1

rooted Vector (root1)

coord1

rooted Vector

coord1

 

rooted Vector (root1)

coord1

rooted Vector (root2)

coord1

error

 

 

rooted Vector (any)

coord1

rooted Vector (any)

coord2

error

 

6

rooted Vector (root1)

coord1

vector field

coord2

v1+v2root1

coord2

7

rooted Vector (root1)

cartesian

position Vector

cartesian

rooted Vector (root1)

cartesian

8

vector field

coord1

vector field

coord1

vector field

coord1

 

vector field

coord1

vector field

coord2

error

 

9

vector field

coord1

position Vector

cartesian

error

 

10

position Vector

cartesian

position Vector

cartesian

position Vector

cartesian

Examples

withVectorCalculus:

Free Vectors can only be added if they are in cartesian coordinates.

1,2,3+1,1,1

2ex+3ey+4ez

(1)

A cartesian free Vector can be added with a rooted Vector

v1RootedVectorroot=1,π,1,1,polarr,t

v111

(2)

v1+1,1

00

(3)

Rooted Vectors can be added if they are in the same coordinate system and are rooted at the same point.

v1RootedVectorroot=1,π2,1,2,polarr,t

v112

(4)

v2RootedVectorroot=1,π2,1,0,polarr,t

v210

(5)

v1+v2

22

(6)

GetRootPointv1+v2

1er+π2et

(7)

When a vector field and a rooted Vector are added, the vector field is evaluated at the root point of the vector and the operation is carried through. The coordinate system of the sum and the vector field are the same.

v3RootedVectorroot=1,π3,π4,0,1,0,sphericalr,p,t

v3010

(8)

vfVectorFieldy,x,z,cartesianx,y,z

vfye_x+xe_y+ze_z

(9)

v3+vf

24+32424+32432+12

(10)

GetRootPointv3+vf

324ex+324ey+12ez

(11)

GetCoordinatesv3+vf

cartesianx,y,z

(12)

Vector Fields can be added if they are in the same coordinate system.

vf2VectorFieldr,t+π,polarr,t

vf2re_r+t+πe_t

(13)

vf3VectorFieldr,tπ2,polarr,t

vf3re_r+tπ2e_t

(14)

vf2+vf3

2re_r+2t+π2e_t

(15)

Position Vectors can also be added, the result is a position Vector.

pv1PositionVectorp,p,polarr,t

pv1pcosppsinp

(16)

pv2PositionVectorp,p2,cartesianx,y

pv2pp2

(17)

pv1+pv2

pcosp+ppsinp+p2

(18)

See Also

VectorCalculus

VectorCalculus[PositionVector]

VectorCalculus[RootedVector]

VectorCalculus[Vector]

VectorCalculus[VectorField]