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visits member for 2 years, 3 months
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Nov
11
comment Why do we have to use an integral in this scenario to figure out $v_{max}$?
In that equation $M$ is the mass enclosed in a Gaussian surface about the center of the Earth. If I remember correctly, the field turns out to go like $GmMr/R^3$ where $R$ is the radius of the Earth.
Nov
9
comment Is the explanation of special relativity in Stephen Hawking's “The Grand Design” flawed?
@bright.magus it's shorthand for $t$ arbitrarily larger than the duration of the experiment.
Nov
9
comment Is the explanation of special relativity in Stephen Hawking's “The Grand Design” flawed?
There are a lot of commonly understood tools in special relativity that have to be sorted: Filling space with clocks at $t=-\infty$ and collecting all the data at $t=+\infty$. So you can talk about "the location at time $t$ in frame $X$" and make perfect sense of it. So saying "two persons can't see the same ray of light" is a bit off.
Nov
5
answered High speed does not kill. Does acceleration do it ? or jerk?
Nov
4
answered Waves in water always circular
Nov
2
comment Can action be unbounded from below?
($\int L$ being $\int_0^tLdt$ given $x=b\cos(t)$)
Nov
2
comment Can action be unbounded from below?
My thoughts: Maybe your numerical scheme doesn't implement boundary conditions properly? Ex: If $L=\dot{x}^2-x^2$, then $x(t)=b\cos(t)$ satisfies the Euler Lagrange equations, but $\int L=-b^2 \cos(t)\sin(t)$ can be made arbitrarily negative by increasing $b$.
Oct
31
comment Understanding the Jacobian Matrix
@ValterMoretti I couldn't figure out any intuition behind it! I guess you still have the eigenvalues of $A$ have to be negative (except in the worst posed problems you'll still have a characteristic equation with $n$ solutions counting multiplicity) but it looks like in the $x''=Ax$ case you can have your eigenvalue negative but your solution blowing up to infinity like $x \sin(x)$! But all of that is really far from an intuitive understanding, so I guess it doesn't belong in the answer. I'd rather just sweep it under the rug.
Oct
28
answered Understanding the Jacobian Matrix
Oct
27
comment Is any energy required to deflect an asteroid, with force always perpendicular to its trajectory?
@stalinbeltran Hence the "if".
Oct
27
revised Is any energy required to deflect an asteroid, with force always perpendicular to its trajectory?
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Oct
26
revised Is any energy required to deflect an asteroid, with force always perpendicular to its trajectory?
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Oct
26
comment Is any energy required to deflect an asteroid, with force always perpendicular to its trajectory?
@stalinbeltran I was satisfied to stop my investigation here: No work is done on the asteroid. A minimum of $mv_1^2(1-\cos(\theta))$ is done on the rocket fuel. This result is due to conservation of momentum. If momentum isn't conserved (say we're modeling the sun as a fixed point w/ a $\frac{1}{r}$ potential), then this result won't hold and it might not take energy to deflect the asteroid.
Oct
24
answered Is any energy required to deflect an asteroid, with force always perpendicular to its trajectory?
Sep
28
comment Do Monte-Carlo updates have a physical significance in stat. mech?
From my very limited experience I think this is an archetypical question and the answer (in general, though specific cases can have real dynamical significance) is no. The goal of detailed balance and ergodicity is to let you get uncorrelated and unbiased samples of your configuration space. That's it.
Sep
24
awarded  Autobiographer
Sep
23
comment What is the mathematical equation for a sine wave?
If someone asked me to give the equation of a sine curve, I would write $\sin(x)$. If someone asked me to describe sinusoidal motion, I would give the equation $A \sin(\omega x+\varphi )$. I think this is a pretty standard way of looking at things (the wiki article does clarify by saying "or sinusoid"). By virtue of the angle addition identities, sinusoidal motion can also be described as $A \cos(\omega x+\varphi)$ or $A \sin(\omega x)+B \cos(\omega x)$, with any replacement of $+$ with $-$ that you want. So if you see these equations they're equivalent to the wikipedia article.
Sep
19
answered Is a causal relationship implied by Newton's 2nd Law?
Sep
14
comment Why Do My Fan Blades Produce Color When They Spin?
@CuriousOne To check that I understand you, would the period of the color cycle correspond to the AC current period passed through it? (If the UV source was constant over time everything should average out)
Sep
14
answered Could $\int (\ddot\phi + \mu\dot\phi^2)d\phi$ ever be negative? How to show it?