Derivation of Euler's equations for rigid body rotation Sorry for using this image, but I thought this was the most convenient way of asking this question. Please zoom in.  I do not understand from the line, "Now, in the body frame $T = (T_{x'}, T_{y'}, T_{z'})\ldots$"  How is that in the body frame? That should be in the inertial frame, since it is dL/dt. In the body frame, it is dL'/dt.   How can you treat dl/dt as the torque in the body frame, and then derive the Euler's equation?
Derivation of Newton-Euler equations I am in search of a simplified version of the derivation of  (both translational and rotational) for a rigid body (3D block) that has a body fixed frame and where the center of mass of the body is not at the center of gravity.  I can find elementary derivations for the same system when the center of mass is at the center of gravity, but not for my system in question.    I am using the derivation as background research for a rotordynamics project that I'm working on.  Any help and or references would be greatly appreciated!  :)
Blender 2.79b is installed (from .exe) on my computer, currently. And I just downloaded the Blender 2.8 release candidate 2 (.zip).  When I create something in Blender 2.8, after I save it, I cannot open it again because the computer tries to open the blend file in version 2.79b. And manually selecting the 2.8 version from zip file does not work.  How can I open my blender 2.8 files? Do I have to delete Blender 2.79b? This is a follow up from this .  I'm using this slightly modified script to enumerate all installed MSI packages:  strComputer = "."  Set objWMIService = GetObject("winmgmts:" &amp; _     "{impersonationLevel=impersonate}!\\" &amp; _     strComputer &amp; _     "\root\cimv2")  Set colSoftware = objWMIService.ExecQuery _     ("SELECT * FROM Win32_Product")     If colSoftware.Count &gt; 0 Then     For Each objSoftware in colSoftware         WScript.Echo objSoftware.Caption &amp; vbtab &amp; _         objSoftware.Version     Next Else     WScript.Echo "Cannot retrieve software from this computer." End If   What is surprising however, is its abysmal performance. Enumerating the 34 installed MSI packages on my XP box takes between 3 and 5 minutes !  By comparison, the Linux box that sits besides is taking 7s to enumerate 1400+ RPMs... sigh  Any clues on this ? Do AWS Reserved Instances need to be assigned to the instance? I have an RDS instance running of type db.t2.small.  I bought a reserved instance for 1 year of the same type, I paid the partial upfront rate.  Do I need to assign this subscription in some way to my existing instance to say 'This is the instance that is using the subscription' or does AWS just charge for the instance usage depending which instances you have running and whether an available subscription was active for it at the time which determines the running rate?  The reason that I ask is that I can't see any mention of the reduced rate on my AWS Billing area and it shows that I've used 17 hours of my reservation, but there isn't a row on my bill so far this month that indicates the new partial upfront rate that I should be charged for my instance. There are a lot of poorly drawn schematics here. A few times people have actually asked for critiques of their schematics. This question is intended as a single repository on schematic drawing rules and guidelines can point people to. The question is  What are the rules and guidelines for drawing good schematics?     Note: This is about schematics themselves, not about the circuits they represent. Zoom in/out on click in OpenLayers 3? "Coming soon" pages & SEO How to calculate number of days between two given dates? Accessing derived class property members from base class object in CSharp Why do I have to enter my password to log in? Using the Stack Exchange login, why do I have to enter my password again and again to log in? Wasn’t the whole purpose of OpenID to do away with this?  This doesn’t even only happen when visiting a new Stack Exchange site – it also happens for sites where I already have an account but which I don’t visit regularly. Here’s what I mean:    Of course I don’t remember my password (it’s a long random string). And so I have to go to my password manager and manually copy the password from openid.stackexchange.com’s account into the login form. – And incidentally, this is what my password manager looks like now:    (And, by the way, those are the only entries in my keychain so far, but by far not the only SE sites where I have an account.)  … I feel that this defeats the purpose of site-wide login and OpenID. In the olden times when MyOpenID was still working properly, I’d simply enter my OpenID on the login form, and the software would take care of the rest – namely, redirect to the OpenID service, (automatically) verify that I was authorised to use it, and redirect back to the original website, having logged me in. It was literally one button click for me. It’s substantially more work now, and I’d like to understand why this regression is necessary.  (Note: of course once a site’s password has landed in my password manager I (probably?) won’t have to enter it again. But still: wasn’t site-wide login and OpenID supposed to solve this already?) Do you use "a" or "an" before acronyms / initialisms? 99% of the time, I'm clear on when I should use "a" versus "an." There's one case, though, where people &amp; references I respect disagree.  Which of the following would you precede with "a" or "an," and why?   FAQ FUBAR SCUBA   [Note: I've read the questions  and , but the rules given there don't necessarily apply here.]    [Edited to add]  Here's a shorter (and hopefully clearer) version of the question…  In written English, which is correct (and why): "a FAQ" or "an FAQ"?  Some references with differing opinions:   an: the  and  a: the Microsoft Manual of Style for Tech Publications, 3e either: the  and I find it intuitive enough that the radical of $\mathfrak{gl}_n\mathbb F$ is the scalar matrices, but I have trouble finding an easy, but complete proof:  Proof. Let $\mathfrak s$ denote the scalar matrices. Clearly $\mathfrak s\subset\mathrm{rad}(\mathfrak{gl}_n\mathbb F)$. Suppose that $\mathrm{rad}(\mathfrak{gl}_n\mathbb F)$ is generated by more than one element, so that $X\in\mathrm{rad}(\mathfrak{gl}_n\mathbb F)$, but $X\notin\mathfrak s$. We can change basis such that $\mathrm{rad}(\mathfrak{gl}_n\mathbb F)$ is upper-triangular. (The change of basis leaves the scalar matrices invariant.) Then $X$ is upper-triangular.  I want to conclude that there exists a $Y\in\mathfrak{gl}_n\mathbb F$ s.t. $[X,Y]$ is not upper-triangular. How can I see that $Y$ always exists, except by waving hands? How do I copy to the clipboard in JavaScript? How to resize array in C++? Let $n\geq 2$ and let $k$ be "considerably larger" than $n$ (like some large multiple of $n$). Then for each $i$ such that $0&lt;i&lt;n$ and $\gcd(i,n)=1$ let's define $$c_i=\left|\{p_j\;|\; p_j\equiv i \mod n,\;\mbox{where $p_j$ is the $j$-th prime, $1\leq j\leq k$}\}\right|$$ so $c_i$ represents how many of the first $k$ primes are congruent to $i$ modulo $n$.  What can we say about $c_i$s, that is about the distribution of the first $k$ primes modulo $n$?  I thought the distribution will be seemingly random, and that is mostly true - for example $c_i$s are always very close together. But there are observable non-random patterns. For example for $n=3$, for various $k$s I've tried  (up to $10^6$) I always got $c_2&gt;c_1$. If this were just some kind of random discrepancy due to distribution of small primes, it would eventually vanish for large $k$s, which I don't observe. Export EDITOR with a flag I'm using Zsh and some CLI's such as Google's gcloud load files via $EDITOR.    For me, I have set this as:  export EDITOR="/usr/local/bin/mvim"   With aliases for that editor using the -v flag which loads vim in the terminal:   mac_vim="$EDITOR -v"  alias vi=$mac_vim  alias vim=$mac_vim  alias v=$mac_vim   That works but when the gcloud CLI calls $EDITOR it does not have the -v flag so it opens in a new terminal.  I thought I could change that by instead adding the -v flag here:  export EDITOR="/usr/local/bin/mvim -v"   However, when I try and run that on the command line I get:  $EDITOR text.html zsh: no such file or directory: /usr/local/bin/mvim -v   Is it possible to include a flag when exporting my $EDITOR? How to `bundle install` when your Gemfile requires an older version of bundler? What's amazing about these open world games is the freedom I have as a player. If I don't want to follow the main story line for a while, and just explore, I can do that, and the game won't break.  On the other hand I don't particularly like the feeling of having made a significant, bad choice in the game, among the lines of Yeah, that dialog option you selected hours ago? This amazing quest line is now off limits.  If I recall correctly, in Morrowind, I had to progress through a few different guilds' quests in the right order, otherwise it'd have stopped my progress in a few guilds.  As a Skyrim example, it doesn't appear that the very first choice made in Helgen at the very beginning has much significance. If someone told me It's not that significant, you still get to choose sides (or, rather not told me "This is important"), that'd help.  Another example: Based on a question I read here, I should probably make sure that I don't throw away any of the dragon priest masks and need to make sure to collect one during a specific quest. This would be relevant for this topic if I could easily miss it otherwise while doing that question.  This includes accidental problems possibly caused by bugs: It appears .  It doesn't matter too much which of the love triangle guys in Riverwood I support: That's not nearly significant enough.    Are there non-obvious, hidden decision points in the quests and story lines? When playing in a certain area, doing a certain quest, what do I need to make sure to do or not do, to not accidentally prevent me from getting or achieving something significant?  I still want to explore on my own, but want to be aware of which choices are important.  This is somewhat related to . Secure hash and salt for PHP passwords It is currently said that MD5 is partially unsafe. Taking this into consideration, I'd like to know which mechanism to use for password protection.  This question,   suggests that hashing multiple times may be a good idea, whereas  suggests using salt.  I'm using PHP. I want a safe and fast password encryption system. Hashing a password a million times may be safer, but also slower. How to achieve a good balance between speed and safety? Also, I'd prefer the result to have a constant number of characters.   The hashing mechanism must be available in PHP It must be safe It can use salt (in this case, are all salts equally good? Is there any way to generate good salts?)   Also, should I store two fields in the database (one using MD5 and another one using SHA, for example)? Would it make it safer or unsafer?  In case I wasn't clear enough, I want to know which hashing function(s) to use and how to pick a good salt in order to have a safe and fast password protection mechanism.  Related questions that don't quite cover my question: Your last flag was declined - no it wasn't Homomorphism between free groups Let $F_a$ be the group which is freely generated by $a$ elements. How to show that there is a homomorphism from $F_a$ onto $F_b$ if and only if $b\le a$?  I was thinking one possibility is if $F_a$ generated freely by $\{x_1, \dots , x_a\}$ and $F_b$ generated freely by $\{y_1, \dots , y_b\}$ then consider map which says $\phi(x_i)=y_i$ for $1\le i \le b$ and $y_1$ otherwise. I do not know if this works or even how to proceed. How to show this fact?