Example 1.
Create the 1st order jet space of 2 independent variables and 2 dependent variables .
Define a vector and compute its total and evolutionary parts totand evol. Check that = totevol
Define a vector and compute its total and evolutionary parts tot and evol. Check that = totevol
Define a vector and compute its total and evolutionary parts tot and evol. Check that = tot evol
Example 2.
In this example we illustrate the geometric interpretation of the evolutionary part of a projectable vector field. First define a 3-dimensional bundle over a two dimensional base. Define the base space separately.
Define a vector field and compute its evolutionary part evolDefine the projection of the vector field onto the base manifold
Calculate the flow of and the flow of .
Define a section of sending .
Calculate the induced flow on the space of sections.
Compare with the components of evol