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

This worksheet 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 give?

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