Coordinate systems visualization
This tutorial illustrates how to visualize multidimensional coordinate systems using Atlas package.
To visualize a coordinate system you can use the
Visualize function with the following syntax:
Visualize[{y1, y2,..., yn}] where
{y1, y2,..., yn} is a list with the coordinate system equations.
If you define the coordinate system equations as a variable like that eqs =
{y1, y2,..., yn} then you have to use the following syntax:
Visualize[Evaluate[eqs]] because the
Visualize function has attribute HoldAll.
You can use any option for native
Mathematica plot functions with the
Visualize function. For instance:
PlotLabel,
ViewPoint etc.
Examples:
| Visualize[{expr1, expr2,..., exprn}] | generates visual presentations of m-dimentional mapping, where m is number of indeterminates in {expr1, expr2,..., exprn} |
Necessary functions.
2-dimensional coordinate systems
Polar coordinate system
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Bipolar coordinate system
Visualization with parameter a as a variable
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Visualization with fixed parameter a
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Maxwell coordinate system
Visualization with parameter a as a variable
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Visualization with fixed parameter a
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3-dimensional coordinate systems
Spherical coordinate system
Visualization as a set of coordinate surfaces
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Visualization in one plot
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SixSphere coordinate system
Visualization as a set of coordinate surfaces
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Visualization in one plot
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Toroidal coordinate system
Visualization as a set of coordinate surfaces
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Visualization in one plot
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N-dimensional coordinate systems
Cartesian coordinate system
The coordinate system equations for n-dimensions. You can change Dim variable here. Remember that visualization of high dimensional objects may take a lot of time and memory.
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Sherical coordinate system
The coordinate system equations for n-dimensions. You can change Dim variable here. Remember that visualization of high dimensional objects may take a lot of time and memory.
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- Lie derivative
- Exterior product
- Tensor product
- Hodge operator
- Covariant derivative
