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):
What we do?
We calculate metric tensor field
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 notebook to save the Mathematica
code (Output.nb by default):
Press FINISH button and execute in Mathematica
the generated file:
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.