Different
Coordinate Systems

This page is a sub-page of our page on • Substitution in integrals.

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Related KMR-pages:

Partial Differential Equations

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Other relevant sources of information:

Coordinate system
Separation of variables in Differential Equations
Orthogonal coordinates
Curvilinear coordinates
Confocal conics sections
Elliptic coordinate system
Parabolic coordinates
Elliptic cylindrical coordinates
Ellipsoidal coordinates
Confocal quadrics
Paraboloidal coordinates
Confocal Ellipsoidal coordinates
Confocal Paraboloidal coordinates

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The interactive simulations on this page can be navigated with the Free Viewer
of the Graphing Calculator.

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Polar Coordinates:


The interactive simulation that created this movie


The interactive simulation that created this movie

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Cylindrical coordinates:


The interactive simulation that created this movie


The interactive simulation that created this movie

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Spherical coordinates:


The interactive simulation that created this movie

The interactive simulation that created the thee movies above.

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Elliptic coordinates:


The interactive simulation that created this movie.

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Parabolic coordinates


The interactive simulation that created this movie.

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Confocal Quadrics


The interactive simulation that created this movie


The interactive simulation that created this movie


The interactive simulation that created this movie


The interactive simulation that created this movie


The interactive simulation that created this movie

Parabolic Cylindrical Coordinates

Parabolic coordinates

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Paraboloidal Coordinates

Confocal Paraboloids acting as mirrors to a planar wavefront

Confocal Paraboloids – reflected Dupin cyclide.gcf

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Reflection of a planar wavefront in a saddle surface
turns the wavefront into a Dupin cyclide
:

Confocal-paraboloids-planar-wavefront-into-cyclide-reflection.gcf

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A set of (horizontally positioned) confocal paraboloids give the same (Dupine cyclide) reflection of a planar wave front that is incident along the vertical axis:

The interactive simulation that created this movie.

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The same variation of the confocal paraboloids mirrors is shown here without the reflected wavefront (which is the same for all the paraboloids of the confocal family:

Confocal Paraboloids – reflect vertical rays into Dupin cyclide.gcf

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