3D Coordinate systems in Atlas 2D/3D Wizard

This notebook illustrates how to use the Atlas 2D/3D Wizard to solve problems in elementary differential geometry. As an example, we discuss changing from Cartesian to Bipolar Cylindrical coordinate systems.

What we have?

3D coordinate system (Bipolar Cylindrical):
z = w

What we do?

We calculate metric tensor field and connection.
We also obtain the Laplace operator and Christoffel symbols.
Run Atlas 2D/3D Wizard and press NEXT button:
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Choose 3D- space and press NEXT button:
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Select BIPOLARCYLINDRICAL coordinate system and press NEXT button:
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Press NEXT button (just coordinate system calculations no curves or surfaces):
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Nothing to enter (no curve or surface selected), just press NEXT button:
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You can skip this step (no data was entered just predefined coordinate system):
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Specify a notebook to save the Mathematica code (Output.nb by default):
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Press FINISH button and execute in Mathematica the generated file:
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You will see the results of the execution in the notebook: metric, connection, Christoffel symbols and Laplace operator.
It takes 45 seconds to solve this problem from the beginning to the end! Just try it.