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seen Nov 24 at 2:14

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Aug
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accepted How do I read the simple, but contradictory, Lagrangian ($\mathcal{L} = x + v$)?
Aug
1
comment How do I read the simple, but contradictory, Lagrangian ($\mathcal{L} = x + v$)?
"This is a crucial property of lagrangians: I can add a total derivative to a lagrangian without changing the equations of motion." That really cool. Can you give an example of how that's useful in a real physical application?
Aug
1
comment How do I read the simple, but contradictory, Lagrangian ($\mathcal{L} = x + v$)?
I think you miss the point. I know that the above Lagrangian is broken, but I don't buy that it's completely meaningless. For example, you could look at what happens as you smear the stationary point into a wider and wider interval. Or you could look at $\mathcal{L} = \alpha x^n + \beta v$ starting with $n = 2$ and observe what happens as $n$ goes to 1. Or you could play with similar limits using $v$. I was hoping people would point me towards illustrative interpretations. Of course the Lagrangian is broken, but many seem to think that unbroken means undiscussable.
Aug
1
comment How do I read the simple, but contradictory, Lagrangian ($\mathcal{L} = x + v$)?
Thanks. I get this sort of stuff, but I'm still confused. For example, division by zero is not just illogical nonsense. A lot can be said about division by zero. Your result diverges to positive or negative infinity. Following this "logical impossibility" can lead you to infinitesimals. I get that this lagrangian is nonphysical. I know it's nonsense. I'm wondering what kind of nonsense it is. Declaring that energy is now x + v clearly breaks everything, but it's not clear to me that it breaks things so hard that we have to stop talking about them.
Aug
1
comment How do I read the simple, but contradictory, Lagrangian ($\mathcal{L} = x + v$)?
Are there any nonclassical motions? I know it's not a physical world -- but what kind of world is it? I don't expect it to behave nicely, but I would expect it to behave somehow.
Aug
1
comment How do I read the simple, but contradictory, Lagrangian ($\mathcal{L} = x + v$)?
I get that -- but it's not clear to me what it means for a physical system to "not have a stationary point". I can picture a system that never comes to rest, where everything accelerates off into the distance forever, but that's still a stationary path in a Lagrangian, isn't it? What are the paths taken in a world with an inconsistent Lagrangian? How do I picture such a world?
Aug
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revised How do I read the simple, but contradictory, Lagrangian ($\mathcal{L} = x + v$)?
added 78 characters in body
Aug
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comment How do I read the simple, but contradictory, Lagrangian ($\mathcal{L} = x + v$)?
Certainly not. I'm trying to understand the formulation in general, and in my experience a good way to understand things is to break them. I was surprised that the lagrangian broke as hard as it did as fast as it did. What sort of world would making $\int dt (x + v)$ stationary correspond to?
Jul
31
asked How do I read the simple, but contradictory, Lagrangian ($\mathcal{L} = x + v$)?
Jun
10
comment What would happen if the Earth was tidally locked with the Sun?
I'm still working on it, among a number of others. It grew a bit, in the telling, and isn't exactly "short" any more. I also seem to have have a bad case of lots of ideas and not enough time... I will certainly let you know if & when I finish it, though.
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answered What are the physics behind the Coriolis effect?
May
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accepted Will a spinning object come to rest?
May
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comment Will a spinning object come to rest?
That's what I thought -- so the sphere can stop spinning, but does it?
May
23
revised Will a spinning object come to rest?
added 154 characters in body