VectorCalculus
+
An overloaded version of Plus that deals with adding Vectors
Calling Sequence
Parameters
Description
Examples
v1 + v2
v1
-
Vector(algebraic); the first Vector to add
v2
Vector(algebraic); the second Vector to add
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.
coord(v1)
coord(v2)
v1+v2
coord
1
free Vector
cartesian
curved
any
error
2
rooted Vector (root2)
coord2
3
vector field
4
position Vector
5
rooted Vector (root1)
coord1
rooted Vector
rooted Vector (any)
6
v1+v2root1
7
8
9
10
withVectorCalculus:
Free Vectors can only be added if they are in cartesian coordinates.
1,2,3+1,1,1
A cartesian free Vector can be added with a rooted Vector
v1≔RootedVectorroot=1,π,1,1,polarr,t
v1≔11
v1+1,1
00
Rooted Vectors can be added if they are in the same coordinate system and are rooted at the same point.
v1≔RootedVectorroot=1,π2,1,2,polarr,t
v1≔12
v2≔RootedVectorroot=1,π2,1,0,polarr,t
v2≔10
v1+v2
22
GetRootPointv1+v2
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.
v3≔RootedVectorroot=1,π3,π4,0,1,0,sphericalr,p,t
v3≔010
vf≔VectorFieldy,x,z,cartesianx,y,z
v3+vf
24+32424+324−32+12
GetRootPointv3+vf
GetCoordinatesv3+vf
cartesianx,y,z
Vector Fields can be added if they are in the same coordinate system.
vf2≔VectorFieldr,t+π,polarr,t
vf3≔VectorFieldr,t−π2,polarr,t
vf2+vf3
Position Vectors can also be added, the result is a position Vector.
pv1≔PositionVectorp,p,polarr,t
pv1≔pcosppsinp
pv2≔PositionVectorp,p2,cartesianx,y
pv2≔pp2
pv1+pv2
pcosp+ppsinp+p2
See Also
VectorCalculus[PositionVector]
VectorCalculus[RootedVector]
VectorCalculus[Vector]
VectorCalculus[VectorField]
Download Help Document
