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Example 1.
Create the jet space for the bundle with local coordinates. We calculate the total part of some vector fields.
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Define a vector and compute its total part.
| (2.2) |
The prolongation of tot(is the total derivativewith respect to
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| (2.3) |
Define a vector and compute its total part.
| (2.4) |
Define a vector and compute its total part.
E >
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| (2.6) |
| (2.7) |
Example 2.
We show that the total part of a vector field annihilates the 1st order contact forms.
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| (2.8) |
J33 >
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| (2.9) |
A total vector field always annihilates the first order contact 1-forms.
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| (2.10) |
J33 >
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A vector field is always the sum of its total and evolutionary parts.
J33 >
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| (2.12) |
| (2.13) |