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DifferentialGeometry

  

ApplyTransformation

  

evaluate a transformation at a point

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

ApplyTransformation(Phi, pt)

Parameters

Phi

-

transformation from a manifold M to another manifold N

pt

-

a list of coordinates or a list of equations defining a point in the domain manifold M

Description

• 

ApplyTransformation(Phi, pt) returns the coordinates of the point Phi(pt) in N.

• 

The second argument is of the form [a1, a2, ...] or [x1 = a1, x2 = a2, ...], where x1, x2, ... are the coordinates on M.

• 

This command is part of the DifferentialGeometry package, and so can be used in the form ApplyTransformation(...) only after executing the command with(DifferentialGeometry).  It can always be used in the long form DifferentialGeometry:-ApplyTransformation.

Examples

withDifferentialGeometry:

 

Example 1. 

Define coordinate systems M and N.

DGsetupx,y,z,M:DGsetupu,v,N:

 

Define a transformation Phi from M to N.

ΦTransformationM,N,u=x2+y2+z2,v=xy+yz+xz

Φu=x2+y2+z2,v=xy+xz+yz

(1)

 

Apply the transformation Phi to the points p1, p2.

p11,2,3

p11,2,3

(2)

ApplyTransformationΦ,p1

14,11

(3)

p2x=5,y=0,z=1

p2x=5,y=0,z=1

(4)

ApplyTransformationΦ,p2

u=26,v=5

(5)
N > 

See Also

DifferentialGeometry

Transformation

PDEtools[dchange]

Physics[TransformCoordinates]

Physics

 


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