Relationship With Vector Fields in The Usual Sense
A vector field in the usual sense can be thought of as a time dependent vector field defined on even though its value on a point does not depend on the component .
Conversely, given a time dependent vector field X defined on, we can associate to it a vector field in the usual sense on such that the autonomous differential equation associated to is essentially equivalent to the nonautonomous differential equation associated to X. It suffices to impose:
for each, where we identify with . We can also write it as:
- .
To each integral curve of X, we can associate one integral curve of, and vice versa.
Read more about this topic: Time Dependent Vector Field
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