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Jun 5, 2020 at 14:09 history closed Alexandre Eremenko
Jens Reinhold
abx
YCor
user44191
Needs details or clarity
Jun 5, 2020 at 12:38 vote accept dza
Jun 5, 2020 at 12:32 answer added Ben McKay timeline score: 2
Jun 5, 2020 at 12:23 comment added Ben McKay If the vector field is continuously differentiable, it has a unique flow line through each point, so the closest path is the unique path. It is as if you were to walk into a room wearing one hat, and ask me which of the hats you are wearing looks best. I would have to answer, the one unique hat are wearing. So it doesn't seem like much of a question.
Jun 5, 2020 at 12:22 history edited dza CC BY-SA 4.0
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Jun 5, 2020 at 12:20 comment added dza @BenMcKay Thanks for the question, it's made me rethink what I originally stated in the question. It would be more like an unpowered boat, with no sail, just a rudder so it would moved strictly by ocean currents.
Jun 5, 2020 at 12:15 comment added Ben McKay Can you only move along the vector field (like a train along a track), or do you have a rudder to steer with (unlike a train, more like a boat)?
Jun 5, 2020 at 12:14 history edited YCor
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Jun 5, 2020 at 12:06 history edited dza CC BY-SA 4.0
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Jun 5, 2020 at 11:36 history edited dza CC BY-SA 4.0
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Jun 5, 2020 at 11:34 comment added dza Thanks to both of you, Leo the first portion of your response is what I was referring to, that you can only move following the vector field. I was interested in finding paths that are as close to, if not all the way to the 2nd point in the vector field.
Jun 5, 2020 at 11:31 review Close votes
Jun 5, 2020 at 14:09
Jun 5, 2020 at 11:14 comment added leo monsaingeon Yes, what do you mean by "within the vector field"? do you mean that one can only move following the vector field? If so the problem is hopeless because two arbitrary points are extremely unlikely to be connected by an integral curve. If not I guess your problem is meaningless and you should reformulate your question.
Jun 5, 2020 at 11:11 comment added Alexandre Eremenko What is the relation between the path and the vector field?
Jun 5, 2020 at 10:28 review First posts
Jun 5, 2020 at 11:22
Jun 5, 2020 at 10:20 history asked dza CC BY-SA 4.0