New answers tagged physics
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Solving challenging 4D integrals arising from triangle-triangle gravitational interaction
I couldn't really find a closed form, I even found the explicit form for the integrand using Sympy and it is a complete monster to integrate. I'm just going to offer you a (maybe?) simpler form of ...
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Given Green's function, can I find the corresponding operator?
Merely reverse the steps that got you there, in the first place.
Your framing your problem in terms of generic Green's functions formalism is superfluous.
I'll be using the direct, mainstream seat-of-...
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Given Green's function, can I find the corresponding operator?
Perhaps somewhat naïve view is to look first at a discrete operator equation
$$
LG=1 \Leftrightarrow \sum_{k}L_{nk}G_{km}=\delta_{n,m}.
$$
This is trivially solved via the matrix inverse:
$$
L = G^{-1}...
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What is the fault in this method of finding second moment of area of a circle
You did not account for the second moment of the triangle itself.
The parallel axis theorem applies, as it always does.
For this purpose you can treat each segment as a triangle with base parallel to ...
- 100k
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Optimal length of rope for sliding across a gap
Too long for a comment.
A way to solve your problem. The considered system is holonomic and can be modeled considering the lagrangian
$$
L = \frac 12 m \|\dot p\|^2-m g y + \lambda\left(y-a\cosh\left(\...
- 34.2k
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Optimal length of rope for sliding across a gap
Trying your problem, what I would suggest first is to write
$$\frac{dt}{da} = -\frac{1}{2\sqrt{a^3g}}\,f(a)$$ As your plot shows, there are values for which $f(a)$ has a complex value and this does ...
- 268k
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How to interpret the condition of a circumference rolling without slipping on another circumference
The circle with center $O$ is not moving, so the velocity of the point of contact must be zero.
Let $P$ be the point on the circle with center $\Omega$ that is initially in contact with circle $O$.
...
- 100k
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How to interpret the condition of a circumference rolling without slipping on another circumference
That is exactly what "without slipping" means. Points in contact have no relative motion. If the two centers are fixed the angular velocity of the small circle will be $\frac Rr$ times the ...
- 377k
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Is there a simple maximally general generalization of Noether's theorem to arbitrary dynamical systems?
Here is a really simple version of Noether's theorem valid for completely arbitrary dynamical systems: if $X$ is a set being acted on by an arbitrary "time monoid" $M$, and $G$ is a group of ...
- 432k
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Galileo transformation group
Mechanis involves an arbitrary MKS-system of gauges for lenghts of point distances in [m], clock reading differences of time in [s] and an arbitrary unit of mass [m].
Its euclidean geometry in the ...
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Calculate azimuth and pitch angle from total angle and direction
Your question is equivalent to the following:
Starting at zero latitude and zero longitude on a sphere of radius $1$, travel a distance $\delta$ in the compass direction $\psi$. What latitude $\phi$ ...
- 100k
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Magnitude of Instantaneous Velocity $=$ Instantaneous Speed Rigorous Proof
Suppose at some initial time $t$ we have a particle whose location is described by the instantaneous position vector $\mathbf{r}(t)$. After a small time increment $\Delta t$, our particle has moved ...
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Physics Kinematics Equation Derivation
The previously posted answers derived the kinematic equation $\Delta x = v_it + \frac{1}{2}at^2$, so I hope that at least one of the provided explanations make sense. The process of getting from $\...
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Physics Kinematics Equation Derivation
In simple cases where the velocity is constant, we can say that $\Delta x = vt$. However, when the velocity is changing, we first have to figure out the average velocity over the time interval, and ...
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Calculating deflection on a beam
I am not sure about the triangular wedge but as a starting point for a rectangular beam it sounds like you need Euler-Bernoulli theory for the deflection of a cantilevered beam.
I think the lecture ...
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