So, I know that this question may be tough to answer, but I am asking this question in all seriousness, and I don't consider myself a newbie...  Lately, I am trying to find a way to "generalize" my approach classical mechanics. Specifically, I need a system that can always guarantee a solution to any problem. In a sense, just like mathematicians like to generalize stuff. For example, if you get a system of linear equations, you can always solve it by using the Gauss method of substitution...  I often have the problem of seeing why the solution provided by the textbook is right, but I don't see why my solution is wrong... I'm guessing this is the motivation behind my quest.  I know a field as big as mechanics is hard to cover with one or two principles, but I need something to always help me set the correct system up, the rest being "just math". So is there a method that yields a uniform system?  I have heard that Lagrangian mechanics can provide something like this, but I'm not sure whether to take it up... Can anyone post their experiences with that?  Lastly, I would add that I am no stranger to advanced math topics. I like linear algebra and multivariable calculus... from my experience learning new math has always enhanced and deepened my understanding of physics. Don't hesitate if you have to offer something... maybe a book or similar resource...
I am looking for a book about "advanced" classical mechanics. By advanced I mean a book considering directly Lagrangian and Hamiltonian formulation, and also providing a firm basis in the geometrical consideration related to these to formalism (like tangent bundle, cotangent bundle, 1-form, 2-form, etc.).  I have , but I would like to go into more details about the [symplectic] geometrical and mathematical foundations of classical mechanics.  Additional note: A chapter about relativistic Hamiltonian dynamics would be a good thing.
Huawei E3272 Ubuntu I have a problem with Huawei E3272 modem. Ubuntu 14.04 does not detect it as a mobile broadband modem. If I put my SIM card into my old modem(E3131) everything works, E3272 is just not detected. I have checked lsusb, and here I can see the system detects it as  12d1:14fe Huawei Technologies Co., Ltd.  but I cannot choose it in my Network Connections.  I tried adding usbserial vendor=0x12d1 product=0x14fe in /etc/modules, but it did not change anything. The same goes for adding   # Huawei E3272  ATTR{idVendor}=="12d1", ATTR{idProduct}=="157c", RUN +="usb_modeswitch '%b/%k'"  in /lib/udev/rules.d/40-usb_modeswitch.rules. I also tried installing Modem Manager, but it did not help.  Have you got any idea what could I do, so my system would detect my new modem? I would like to be able to use LTE. :) Google Search Console domain property not in the list of properties I can add to Google Analytics How do you clear a stringstream variable? I've tried several things already,  std::stringstream m; m.empty(); m.clear();   both of which don't work. When can we find holomorphic bijections between annuli? Quantum entanglement faster than speed of light? Do $T$-invariant subspaces necessarily have a $T$-invariant complement? In unix server grep -r option is not working. OS is HP-UX.  If grep -r is not working any alternative way to do recursive search without -r option? Logistic regression vs. LDA as two-class classifiers Modular arithmetic: division, fractions, solving linear congruences I want to ask a question about modular arithmetic. I know, that modular multiplicative inverse exists only if modulo and integer are relatively prime. I want to know, are there any ways of division in modular arithmetic, if modulo and integer aren't relatively prime? I tried to find info about that, but failed. How to develop intuition for conditional probability? What is the fundamental group of $(\mathbb{C} \setminus {\{0\}})~/~\{e,a\}$, where $e$ is the identity homeomorphism and $az = -\bar{z}$?  Clearly this is homeomorphic to the half cylinder , which is homotopy equivalent to the half circle.  But what is the fundamental group of the half circle? I am a British national living in Spain and my passport is either lost or stolen. I noticed this two days ago when I was intending to take a trip to Salzburg. As it happens, I managed to travel using my UK Driver's Licence. I think a severe mistake was made, as was pointed out to me in Austria, but as they were Schengen Countries, apparently all that is needed is a proof of identity, not a 'travel document'.  My question, therefore, is this. I have business trips over the next three weeks taking me from Spain to Germany, Czech Republic, Austria, and Italy, then back to Germany, and then to the UK. If I obtain an Emergency Passport from the Consulate here in Barcelona, would this be valid as an identity document within Schengen, before I eventually 'cash it in', so to speak, as a travel document when I make my trip from Germany to the UK?  I am hoping so, as I don't fancy my chances of getting back to the UK in time to secure an appointment for a fast-track passport. I am going to call the consulate tomorrow, but would appreciate any advice or prior experience. When is unbalanced data really a problem in Machine Learning? We already had multiple questions about unbalanced data when using , , ,  and a number of other similar questions, what makes it a very popular topic! Unfortunately, each of the questions seems to be algorithm-specific and I didn't find any general guidelines for dealing with unbalanced data.  Quoting , dealing with unbalanced data     (...) heavily depends on the learning method. Most general purpose   approaches have one (or several) ways to deal with this.   But when exactly should we worry about unbalanced data? Which algorithms are mostly affected by it and which are able to deal with it? Which algorithms would need us to balance the data? I am aware that discussing each of the algorithms would be impossible on Q&amp;A site like this, I am rather looking for a general guidelines on when it could be a problem. How is it, that $\sqrt{x^2}$ is not $ x$, but $|x|$? As far as I see, $\sqrt{x^2}$ is not $x$, but $|x|$, meaning the "absolute". I totally get this, because $x^2$ is positive, if $x$ is negative, so $\sqrt{y}$, whether $y = 10^2$ or $y = -10^2$: $y$ is positive.  But then I remember that $\sqrt(x)$ is the same as $x^{1/2}$ and thus, $\sqrt{x^2}$ is the same as $x^{1}$.   So, as far as I get it, $\sqrt{x^2} = x^{2/2}$.  But then, I can cancel $\frac{2}{2}$ to $1$. So: $\sqrt{x^2} = x^1 = x$.  Where does the absolute value in this derivation of the calculation come from?  I get it why its there: Because $(-x)^2 = x^2$, so the radicand is always positive. But from $\sqrt{x^n} = x^{n/2}$ I dont understand how it gets there. I'm using 13.04 for the first time and I am using proxy base server that's why I can't download anything while I use apt-get update then it shows this message  coolmonter@coolmonter-HP-ProBook-4431s:~$ apt-get update E: Could not open lock file /var/lib/apt/lists/lock - open (13: Permission denied) E: Unable to lock directory /var/lib/apt/lists/ E: Could not open lock file /var/lib/dpkg/lock - open (13: Permission denied) E: Unable to lock the administration directory (/var/lib/dpkg/), are you root?   any suggestion Forced to Quit PhD although the hard and proved work If $a_{ij}=\max(i,j)$, calculate the determinant of $A$ I know than an ellipsis can be used to show a broken sentence, the same way an em dash can be used. What I don't know is that if the two are interchangeable and it is writer preference or if different meaning is conveyed by their use.  Are ellipses and em dashes commutable? Is there an official list of Disney Princesses? How to find out who deleted some data SQL Server My boss had a query from a customer yesterday asking how they could find out who deleted some data in their SQL Server database (it is the express edition if that matters).  I thought this could be found from the transaction log (providing it hadn't been truncated) - is this correct? And if so how do you actually go about finding this information out?