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changecoords

change expression in cartesian coordinates to a new coordinate system

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

changecoords(expr, vars, coord, new_vars)

Parameters

expr

-

expression

vars

-

list of 2 or 3 variables

coord

-

name; new coordinate system

new_vars

-

(optional) list of 2 or 3 variables

Description

• 

The changecoords(expr, vars, coord, new_vars) calling sequence changes the expression expr in cartesian coordinates vars to an expression in the new coordinate system coord. The new expression is written in terms of the original variables. An optional fourth argument new_vars can be used to specify the set of variables for the new coordinate system.

• 

The argument coord must be from the set of accepted coordinate types.

  

In three dimensions:

bipolarcylindrical

bispherical

cardioidal

cardioidcylindrical

casscylindrical

confocalellip

confocalparab

conical

cylindrical

ellcylindrical

ellipsoidal

hypercylindrical

invcasscylindrical

invellcylindrical

invoblspheroidal

invprospheroidal

logcoshcylindrical

logcylindrical

maxwellcylindrical

oblatespheroidal

paraboloidal

paraboloidal2

paracylindrical

prolatespheroidal

rosecylindrical

sixsphere

spherical

tangentcylindrical

tangentsphere

toroidal

  

In two dimensions:

bipolar

cardioid

cassinian

elliptic

hyperbolic

invcassinian

invelliptic

logarithmic

logcosh

maxwell

parabolic

polar

rose

tangent

 

• 

The conversions from the coordinate systems to cartesian coordinates are listed in the help page for coords.

• 

New coordinate systems can be introduced by using the addcoords routine. Once introduced, they are recognized by the changecoords command.

• 

See also the plots[changecoords] command.  Note that issuing with(plots) rebinds the name changecoords, so :-changecoords must be used to run this command.

Examples

changecoordsx2+y2,x,y,polar

x2cosy2+x2siny2

(1)

changecoordsx2+y2,x,y,polar,r,θ

r2cosθ2+r2sinθ2

(2)

changecoordsxy,x,y,logarithmic

lnx2+y22arctanyxπ

(3)

changecoordsxyz,x,y,z,bipolarcylindrical

sinhysinxzcoshycosx2

(4)

changecoordsxy+xzy,x,y,z,tangentcylindrical,u,v,w

u3w+uv2wu2vv3+uvu2+v22

(5)

changecoordsxyz,x,y,z,spherical,r,θ,φ

r3sinφ2cosθsinθcosφ

(6)

See Also

addcoords

coords

plots[changecoords]

polar

 


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