Adding legends to tikzpicture
Legend in tikzpicture
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!  :) I have a few satellites and stations orbiting my planets, but I'd like to add onto them. I've seen numerous videos on using docking clamps to attach my new ship to the existing station, but can I do that on a part-by-part basis? For example, I take an extra fuel tank up there, can I attach just the tank to my station, then send my vessel back to Kerbin? I'm not talking about refueling, but rather transferring individual parts from my ship to the station in orbit.  I'd prefer to not have to use an unmanned probe and jettison everything but the desired part in space after docking if possible, but if that's the only way I guess I don't have a choice. I run a guest ubuntu 12.04 on a host ubuntu 12.04, with VirtualBox, and the guest is much, much slower than the host (ALT+TAB takes 4-5 secs). I had a look around and I found contradicting opinions on VirtualBox versus VMware (free); so I thought to keep the former.   Both systems are updated, I installed the additions on the guest and I evenly split memory and video memory (64MB) between guest and host. I am running a Toshiba m200 laptop with 4GB ram and shared video memory. The host bios does not include a configuration option for machine virtualization. I have 2 cpus and I can't give them both to the virtual machine.  Is there anything I overlooked that could solve my problem?  Feel free to ask for more info, and thank you for any help.  EDIT Idling with the system monitor open the (single) guest cpu never gets below 55% and could rise to 80 - 90% just by moving the mouse around. Opening Firefox will cause the system monitor to show cpu usage 100% in the guest, while the host shows that both cpus are evenly working around 60%.  My cpu is Intel® Core™2 Duo CPU T5450 @ 1.66GHz × 2.  If this is not a configuration problem, does it mean my machine is too weak for virtualization? How can I send single file to multiple remote sites at the same time? Can scp be used to send a single file to multiple remote servers at the same time? If so, how? If not, what's the alternative? Input field value - remove leading zeros I have a textbox in Javascript. When I enter '0000.00' in the textbox, I want to know how to convert that to only having one leading zero, such as '0.00'. What was the meaning of the Night King's message? In S08E01 of Game of Thrones, we see this message:    We have seen this several times, the symbol drawn with horse heads, the stones around the Weirwood where White Walkers are created and in some caves, drawn by Children of the Forest.  Do we know the meaning behind this symbol? Does it or something similar occur in the books as well? What determines how much experience I get from a hearthstone match in play mode? Sometimes I win handily and get a little experience, sometimes I squeak out a victory and get a lot.  How is experience earned? Is there any way I can specify a standard or custom numeric format string to always output the sign, be it +ve or -ve (although what it should do for zero, I'm not sure!) How do I get the logged in user's window's credentials in a WPF application Can an html element have multiple ids? Why doesn't the "zig-zag" comb deformation retract onto a point, even though it's contractible? I am starting to read Hatcher's book on Algebraic Topology, and I am a little stuck with exercise 6(c) in Chapter $0$. Unfortunately a picture is involved so it doesn't quite make sense for me to repeat it here - but I'll do it anyways (maybe it helps)     Let $Z$ be the zigzag subspace of $Y$ homeomorphic to $\mathbb{R}$ indicated by the heavier line in the picture:       Show there is a deformation retraction in the weak sense of $Y$ onto $Z$, but no true deformation retraction."   Now the definition for deformation retraction and weak deformation retraction as as follows:  We say that $f: X \to X$ is a deformation retraction of a space $X$ onto a subspace $A \subset X$ if there exists a family of maps $f_t : X \to X$ with $t \in [0,1]$ such that $f_0 = \mathbb{1}$ (the identity) and $f_1 (X) = A$ and also $f_t$ restricts to the identity on $A$ for each $t$.   A weak deformation retraction is almost the same, only that we now relax the conditions $f_1(X) = A$ to $f_1 \subset A$ and, for each $t \in [0,1]$ we require that $f_t(A) \subset A$.  Hence, as far as I understand the question and the concepts involved, I need to show that basically no map can be constructed such that the bold zigzag - line stays put while the thin lines retract to the bold line over a finite time interval $0 \leq t \leq 1$. However, I should be able to show that I can pull the thin lines continously onto the thick line, provided I am allowed to move points on the zigzag line .. is that correct ?  Now, the problem is I can't see why I shouldn't be able to do the former, given that I could find a weak deformation retract. Any help would be great! Override iTunes "media" keys (play, pause, etc) for Spotify? How can I check the actual size used in an NTFS directory with many hardlinks? On a Win7 NTFS volume, I'm using cwrsync which supports --link-dest correctly to create "snapshot" type backups. So I have:  z:\backups\2010-11-28\cygdrive\c\Users\... z:\backups\2010-12-02\cygdrive\c\Users\...   The content of 2010-12-02 is mostly hardlinks back to files in the 2010-11-28 directory, but there are a few new or changed files only in 2010-12-02. On linux, the 'du' utility will tell me the actual size taken by each incremental snapshot. On Windows, explorer and du under cygwin are both fooled by hardlinks and shows 2010-12-02 taking up a little more space than 2010-11-28.   Is there a Windows utility that will show the correct space acutally used? Negative R squared contradicts ssa/sst? I understand from this question -    that the R squared value of a linear regression model can be negative if the intercept is constrained. And this makes sense if you define R squared as -   $$R^2 = 1-\frac{SSE}{SST}$$  One says $SSE&gt;SST$. But then,  $$SST = SSA + SSE $$ Total Sum of squares  = Sum of squared errors + Sum of squared residual. And with this we get -  $$R^2 = \frac{SSA}{SST}$$ And now it is hard to imagine how $R^2$ can be negative. Aren't SSA and SST >0 always? Why don't elves have more babies? Are Lorentz transformations linear transformations? My textbook says that Lorentz transformations are linear transformations and present them as matrices. Lorentz transformations relate different coordinate systems with each other. It seems that coordinate systems are linear spaces, but coordinates are just labels for spacetime points, with no other structures attached. So what is the linearity all about? Is there any way to find out if a file is a directory?  I have the file name in a variable. In Perl I can do this:  if(-d $var) { print "it's a directory\n" } Traveling without paying lodging fees in America I want to travel around the East Coast without paying for lodging.  I'd be willing to sleep in my car or even pitch a tent somewhere. Is this a problem?  Legal?  I really want to get to the beach this season but I’m afraid that lodging will be out of my price range.  Specifically Maryland, Delaware, maybe New Jersey or Virginia. How to install a list of packages using apt-get? The following quote from  assumes "the URL" comes from somewhere and uses it to restrict the Host header. Where does "the URL" come from? Is it from the first line of a HTTP request (e.g. after GET), or from the input to a web client (e.g. an argument to curl, or the input in the address bar of a web browser)? Thanks.     The Host header specifies the Internet host and port number for the   resource being requested, as obtained from the original URL:  Host = "Host" ":" host [ ":" port ]       In particular:      • If the Host header does not contain a port, the default port for the   scheme is assumed.      • If the URL contains an IP address, the Host header should contain   the same address.      • If the URL contains a hostname, the Host header must contain the   same name.      • If the URL contains a hostname, the Host header should not contain   the IP address equivalent to the URL’s hostname, because this will   break virtually hosted servers, which layer multiple virtual sites   over a single IP address.      • If the URL contains a hostname, the Host header should not contain   another alias for this hostname, because this also will break   virtually hosted servers.