2-D Coordinate Systems - Maple Programming Help

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2-D Coordinate Systems

Main Concept

The Cartesian coordinate system is the default 2-D coordinate system used by Maple.

Additionally, Maple supports the following 2-D coordinate systems:

bipolar

cardioid

cassinian

elliptic

hyperbolic

invcassinian

invelliptic

logarithmic

logcosh

maxwell

parabolic

polar

rose

tangent

 

 

Conversions

The conversions from the various coordinate systems to cartesian (rectangular) coordinates in 2-space

u,vx,y

  

are given by:

bipolar (Spiegel)

  

x=sinhvcoshvcosu

  

y=sinucoshvcosu

cardioid

  

x=u2v22u2+v22

  

y=uvu2+v22

cartesian

  

x=u

  

y=v

cassinian (Cassinian-oval)

  

x=a2ⅇ2u+2ⅇucosv+1+ⅇucosv+12

  

y=a2ⅇ2u+2ⅇucosv+1ⅇucosv12

elliptic

  

x=coshucosv

  

y=sinhusinv

hyperbolic

  

x=u2+v2+u

  

y=u2+v2u

invcassinian (inverse Cassinian-oval)

  

x=a2ⅇ2u+2ⅇucosv+1+ⅇucosv+12ⅇ2u+2ⅇucosv+1

  

y=a2ⅇ2u+2ⅇucosv+1ⅇucosv12ⅇ2u+2ⅇucosv+1

invelliptic (inverse elliptic)

  

x=acoshucosvcoshu2sinv2

  

y=asinhusinvcoshu2sinv2

logarithmic

  

x=alnu2+v2π

  

y=2aarctanvuπ

logcosh (ln cosh)

  

x=alncoshu2sinv2π

  

y=2aarctantanhutanvπ

maxwell

  

x=au+1+ⅇucosvπ

  

y=av+ⅇusinvπ

parabolic

  

x=u22v22

  

y=uv

polar

  

x=ucosv

  

y=usinv

rose

  

x=u2+v2+uu2+v2

  

y=u2+v2uu2+v2

tangent

  

x=uu2+v2

  

y=vu2+v2

 

Explore by choosing from the different functions and coordinate systems. Adjust the sliders to change parameters such as the domain and the linear factor of the selected function.

Function:

Coordinate System:

 

 

 

 

Lower limit of Domain, x1

Upper limit of Domain, x2

 

Linear Factor, a

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