
Help with mechanics, energy -- upper division/graduate level.
How does Landau move from the second line to the third line in this proof of the expression for energy? Is that a coefficent of friction in there?

How does Landau move from the second line to the third line in this proof of the expression for energy? Is that a coefficent of friction in there?
This applies whether you swallow the semen orally or take it vaginally. Sex is not a harmless event for your body, in truth. I am legitimately wondering if people are honestly aware of this or not. I think many people are under the impression that swallowing semen doesn't modify your gene expression -- which is an incorrect assumption.
I don't believe many people would be willing to engage in the kind of sexuality that many do engage in if they knew the truth and/or facts about the effects of sex on their biology.
https://www.medicalnewstoday.com/articles/250190
https://pmc.ncbi.nlm.nih.gov/articles/PMC7081221/
Once these genetic changes occur from another man's semen, that very woman is in some sense ruined or soiled for any other man. It's not a low stakes event, it's not a nuetral thing to do -- it's not harmless.
"An additional and intriguing twist is that the effects of semen proteins can favor the interests of males whilst generating costs in females, resulting in sexual conflict."
Men who go around modifying multiple womens genetics are assholes for screwing the dating market for other men. Monogomy was a norm for a reason, it wasn't about abusing it was because of the facts of biology that semen modify women's bodies and behavior. More than anything, I just want to raise awareness about this biology so that people are aware of these facts (facts which promiscuous men will not bother to you, because they're likely narcissists (btw)) so that people can make informed decisions based on biological reality. It's not innocent to ingest semen, and it's not harmless. Just please educate yourself and be aware of the biological facts.
I'm trying to decide whether or not I shoukd continue taking saw palmetto. I take a 400mg whole berry (not concentrate) daily and it has a big effect. There are notacible chnages, both physical and mental (especially with regards to fat distribution (especially on the chest), hair line and water retention in the face, depressed mood and when I first took it digestive irritation).
I'm starting to think that maybe I don't want to take it anymore. My dad hasn't had issues with enlarged prostate and he's over 65 now. I've heard that 5-alpha reductase and maybe DHT can cause harm in the body -- collagen breakdown, hair miniturization and prostate enlargement. So I'm on the fence.
Prostate enlargement is a major problem, it basically disables/debilitates men. They can't even pee. I would like to prevent that, but on the other hand, I dom't want to have depressed mood anymore. And my face looks puffy with elevated estrogen from blocking 5-alpha reductase.
I don't care much about the hair anymore, since I have a beard.
I just want to make sure stoping it isn't going to cause harm in the body or facilitate normal biological aging.
I've been taking DHT blockers since I was 19 years old, for context. Since my hair began receding at 19 years old. Also, I grew a full beard at 17 years old (for context). My mom's side's dad was balding unfortunately. So I seem to have high DHT naturally, and my dad didn't bald, so I may have higher DHT than my dad's family which means that just because he didm't have enlarged prostate issues it doesn't mean that I won't. In fact, if my DHT is high enough to recede my hairline and grow a beard at 17, I would think that maybe odds are high that if I stop taking DHT blockers that maybe I'll eventually have an enlarged prostate (which I don't want).
https://www.sciencedirect.com/science/article/abs/pii/S1078143917305008 <-- this confirms that there is a positive correlation between MPB and BPH. So now I don't know what to do. Medical research doesn't understand the pathway to BPH so I can't take a more targeted approach than just sweepingly blocking 5-ar. I don't have BPH, but blocking 5-ar has problems of its own.
Taking the 5-ar blockers lets me control both hair and prevent prostate enlargement, but the side effects of 5-ar blockers are unavoidable.
Also for reference 5-ar causes genitilia differentiation at birth, or something like that. So it's a main component of sexual dimorphism. So actually low 5-ar is impaired virility. But this then suggests that sexual dimorphism is a main component of building in death into genetics. Because the thing that dimorphs sex is what causes aging in some specific ways, like BPH.
They seem like the same thing, a measure of mass times tangential velocity -- just like linear momentum is the same as linear inertia = mass times (linear) tangential velocity.
Can someone explain to me why, philosophically, least action is required of real motion? I don't see why it is required, but I don't know the reason physics requires it in the first place or at least classical mechanics requires it in its euclidean model of reality.
This is like borderline vector calculus/differential geometry/differential equations. I know for a uniform circle, acceleration points inward. But for non uniform rotation, it doesn't point inward (see screenshot). The idea is that acceleration varies through the path, for a example a ball attached to a string swinging vertically such that gravity is added to its centripital acceleration to create a varying acceleration accross the path of the ball -- even with a fixed radius. You could show this with a vector field.
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The radius is still fixed, so the only thing that varies is the rate of change of the angular speed. If angular speed = √v•v = wr, where v = dr/dt = -rwsin(w)e1 + rwcos(w)e2 = rw(-sin(w)e1 + cos(w)e2), then how do I write a = dv/dt if the rate of change of velocity is non-uniform due to an external force field (like gravity)? Do I do d(v + F)/dt where F is a force field like gravity? Or do I do d(v×F)/dt? Can I differentiate curl?
d*r*/dt = -w^2 rcoswt*e1* - w^2 rsinwt*e2*.
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wt is the change in angle over time as the radius rotates. But why is the w pulled out as a constant for the derivative with respect to time? I don't understand that part.
I don't want the Halitonian formulation, I just want a Newtonian mechanics book that uses the the theory of differential equations to crunch vector calculus in R^3 for apriori unknown parametrizations for physical systems/objects to use Newton's laws in the fully general way in physical space.
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For example, a race car in motion. A basketball shot into a hoop. A bird flying. Etc. Are there any mechanical engineering textbooks that do this maybe? Physics books? Niche applied math books? Anything?
For example, something along these lines: https://youtu.be/p_di4Zn4wz4?is=lO1fnR5_cT9pS_IN.
Which looks better, a masculine bald guy, or a full head of hair?
I've got a simple 2d motion: no vertical acceleration. Net horizontal acceleration varies with time, from 0s to 6s, a = 6m/s. From 6s - 8s, a = 0 and v > 0. Then for an unknown mumber of seconds a < 0 until v = 0. This is a car starting at a stop sign, accelerating for 6 seconds, coasting for 2 seconds and then braking for a second stop sign. My job is to find the distance between the stop signs, after finding the time for the 3rd interval of acceleration.
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I've tried to model position at x(t) = x0 + v0t + 1/2at^2, since x''(t) = a. But doing this gives me 0 distance for the interval from 6s - 8s even though v(t) > 0 from 6s to 8s so something is wrong with the model.
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I'm using vector line integrals to find distance as S v(t) • v(t).
Night sex is stupid, as it sleep deprivee not only you but also your neighbors. Sleep deprivation harms health. It's that simple.
We don't live in the stone age anymore, we don't need night sex. It's not a secret anymore, modern walls are thin. Sleep better, live longer.
Do the signs of the diagonals for the matrix associated with the quadratic form still classify the form if the basis of the columns is non orthogonal? By row reducing rather than solving for an eigenbasis.
I know how to classify quadratic forms in orthogonal diagonalization, but that's too much work to compute. Non orthogonal diagonalization is faster and easier. I have seen completing the square being used, so I would think that a non-orthognal trace could also be used, but I don't have enough time to work through it right now. This is not for a class.
Is it just the same as Sylvester's Criterion (sequence of principle minor determinants) because the pivots along the diagonal are the principal minor determinants? If this is true, then I'm actually starting to think that an eigenbasis is actually a special case of Sylvester's Criterion where you solve for the charachterisitic polynomial roots rather than just a general determinant.
Anyway, since the peincipal minors are the pivots, and since the signs of the principal minors are what classify the quadratic form, I guess the answer to my question is "yes" the signs of a non-orthogonal diagonalization can classify a quadratic form -- speeding up the classification by a lot.
They went through a hot wash by accident. Found them magnetized sticking to the side of the dryer (loool). Let them sit overnight and they sound better than ever. xD Case is still magnetized BTW. Imo an upgrade. It now sticks to fridge doors, and the back of the phone.