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bio website natesoares.com
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age 24
visits member for 2 years, 11 months
seen Aug 6 '13 at 12:50

Jul
2
awarded  Curious
May
21
awarded  Popular Question
Sep
13
awarded  Yearling
Aug
2
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
1
revised How do I read the simple, but contradictory, Lagrangian ($\mathcal{L} = x + v$)?
added 78 characters in body
Aug
1
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.
Jun
10
awarded  Popular Question
May
30
awarded  Teacher
May
29
answered What are the physics behind the Coriolis effect?
May
23
accepted Will a spinning object come to rest?
May
23
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
May
23
comment Will a spinning object come to rest?
I don't think that's the case. If it were, then how does the earth tidally lock the moon? Can't the total angular momentum of the system be preserved in the particles of the sphere while the sphere itself stops spinning? You're absolutely correct for point-particle spheres (though it's not clear what it means for a point particle to spin), but I'm wondering about the internal stresses of macroscopic spheres, and whether there is a force resisting the rotation.