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VectorCalculus

  

AddCoordinates

  

add a new coordinate system

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

AddCoordinates(newsys, eqns, owrite, global)

Parameters

newsys

-

symbol[name, name, ...]; specify the name of the new coordinate system indexed by the names of the new coordinates

eqns

-

list(algebraic); specify the expressions relating the new coordinate system to cartesian coordinates

owrite

-

(optional) equation of the form overwrite=t where t is either true or false; specify whether to overwrite an existing system in the coordinate tables

global

-

(optional) equation of the form addtoglobal=t, where t is either true or false; specify whether to add coordinate system to the global coordinate system tables

Description

• 

The AddCoordinates(newsys, eqns, owrite, global) command adds a new orthogonally curvilinear coordinate system to the VectorCalculus package. This new system can be used in the same way as the other built-in coordinate systems.

• 

If the owrite argument is specified, it must be the name overwrite or an equation of type identical(overwrite)=truefalse. The default is overwrite=false.

• 

If a coordinate system already exists with the same name as in newsys, the owrite parameter determines whether the old system is overwritten. If the old system is not overwritten, an error is raised.

• 

If the global argument is specified, it must be an equation of type identical(addtoglobal)=truefalse. The default is addtoglobal=true.

• 

If addtoglobal=true, then the specified coordinate system is also added to the global coordinate system tables and in consequence will be available in the plots package.

• 

Note that the global coordinate system table only supports 2 or 3-dimensional coordinate systems with a maximum of 3 parameters.

• 

Before calling AddCoordinates, place assumptions on the variables or use the assuming keyword. This assists computations, as more information is recognized for the possible values of the coordinates of the new system.

Examples

withVectorCalculus:

assume0<r&comma;0&theta;&comma;&theta;<2&pi;

AddCoordinates&apos;mypolar&apos;r&comma;&theta;&comma;rcos&theta;&comma;rsin&theta;

mypolar

(1)

Laplacianfr&comma;&theta;&comma;&apos;mypolar&apos;r&comma;&theta;

r~fr~&comma;&theta;~&plus;r~2r~2fr~&comma;&theta;~&plus;2&theta;~2fr~&comma;&theta;~r~r~

(2)

assume0u&comma;0v

AddCoordinates&apos;foo&apos;u&comma;v&comma;u2&plus;v2&comma;u2v2

foo

(3)

FVectorFieldfu&comma;v&comma;gu&comma;v&comma;&apos;foo&apos;u&comma;v

F:=fu~&comma;v~e&lowbar;u&plus;gu~&comma;v~e&lowbar;v

(4)

DivergenceF

182v~u~fu~&comma;v~2&plus;2u~v~gu~&comma;v~2u~v~

(5)

See Also

assume

assuming

VectorCalculus

VectorCalculus[Divergence]

VectorCalculus[GetCoordinates]

VectorCalculus[Laplacian]

VectorCalculus[SetCoordinates]

VectorCalculus[VectorField]

 


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