# All Questions

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### Reference Request: Classical Mechanics with Symplectic Reduction

I am trying to find a supplement to appendix of Cushman & Bates' book on Global aspects of Classical Integrable Systems, that is less terse and explains mechanics with Lie groups (with dual of Lie ...
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### Showing a fourth rank tensor in $\epsilon$'s reduces to one in the metric $g$

Consider the fourth rank tensor $$S_{\mu \nu \rho \sigma} = a(\epsilon_{\mu \sigma}\epsilon_{\nu \rho} + \epsilon_{\mu \rho}\epsilon_{\nu \sigma})f(x^2),$$ in 2D where $a$ is a constant and $f(x^2)$ ...
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### Bloch theorem, Energy, Free electron

I'm trying to learn on my own a bit of solid physics to tackle semiconductors afterwards. I'm struggling with the Energy versus $k$ diagrams for a free electron which shows that for a single value of ...
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### Airplane on a treadmill [duplicate]

I've heard conflicting answers, and would like to see the record set straight: An jet/propeller airplane is traveling on a giant treadmill at takeoff speed. Will the plane takeoff, or will it remain ...
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### What is the speed of light from a star moving towards a observer.? [duplicate]

We can say that in vacuum speed of light is constant. But if the star is moving with a certain velocity does it add that velocity to the velocity of photons emitted out of that star?
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### hydraulic scissor jack lifting capacity

Can you please assist with a really simple question? I have a hydraulic scissor jack table with the following: 2 hydraulic cylinders, each with a cylinder stroke of 240mm, a cylinder bore of 50mm ...
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### calculating electrodynamic momentum of a dumbbell (consisting of two point charges) in longitudinal motion

I'm working through a paper on momentum in electrodynamics that requires the integration below and would greatly appreciate any help. I'm pretty sure it evaluates to $2/d$ but I can't quite figure ...
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### What is the idea behind counting the number of excited states and the representation of a group ?

While reading Polchinski's Chapter 1, I encountered the following on page 24, "For example, the $(D-1)$ dimensional vector representation of $SO(D-1)$ breaks up into an invariant and a $(D-2)$-vector ...
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### Which function denotes the energy of thermal motion within a system?

In thermodynamics, the heat $Q$ is defined as a type of energy in transfer, and is not a state function, which function denotes the energy of thermal motion within a system? 1) $TS$, (there is a ...
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### Explanation for $M{\ddot{r}}=-\nabla \phi$

Could someone please explain this equation $$M\bf {\ddot{r}}=-\nabla \phi$$ Where $\bf r$ is a position vector and $\phi$ is the potential function. Could someone brief explain the potential function ...
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### Force problem related to adhesive and bonding

I have two PCBs (printed circuit board), and they are glued by adhesives, as show in the pictures. And the location of the adhesives are indicated on the picture (please notice that NO adhesive is ...
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### How to determine direction of forces in a static problem?

I am consistently getting this wrong. To me, in the picture below, it would make sense that the structure would be pulling downward, and the cable BD would be pulling upward - thus the system is in ...
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### parity invariance of Einstein, Maxwell and Dirac Lagrangians

How can we show that Einstein, Maxwell and Dirac Lagrangians are parity invariant?
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### Why doesn't water in water barometer boil?

I have read that the pressure in a water barometer at the top of the water column is around 0.5 psi and at such low pressures water should boil at around ~26°C (Room temperature). [1] [2] How ...
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### Negative energy/mass bounds on de-Sitter spacetime

There exists a Positive Energy theorem for General Relativity in Anti-de Sitter and asymptotically flat spacetimes, but there is no equivalent theorem for de Sitter spacetimes Question: Is there ...