Let's consider a system described by this simple equation:  $x^{2}+y^{2}=5$  this represents a holonomic constraint. Suppose I would like to reduce the degrees of freedom of this system, I should be able to do it since is described by a holonomic constraint. However, both $x^{2}$ and $y^{2}$ are not invertible. So how can I write one of them as a function of the other?
I'm trying to understand how it's possible to always reduce the degrees of freedom of a system represented by $n$ coordinates $q_{i}$ for which holds $f(q_{1},...,q_{n})=0.$  For example, let's consider the system represented by $x+\cos y=5$. How can i show that this system has only 1 degree of freedom?
Does a card that affects 'each' creature affect creatures that enter the battlefield after it resolves? What command should I use to rotate wood to S,N,W,E,D and U?  I read the entire world edit guide and tried some things but all the results are not satisfactory. Auto-mounting network shares per user I have a server that has a number of CIFS shares that need to be accessed on a per-user basis. For example, I have a Music share which I have full access to, but my wife has read-only access.  When either myself or my wife log into our Ubuntu 11.04 laptop I would like these shares to be automatically mounted per user. Now I understand that if I mount as -t cifs without specifying a user then it will use the USER environment variable. However, I also need to specify a password, so how can I do that when each user has a different password?  I think my questions are:   Is there a way for me to have a per-user /etc/fstab? If not, is there a way to specify that a mount is only applicable to a certain user? Also, the share password is always the same as the local password. Is there a way to specify that this password should just pass through from the client to server rather than having to specify it in a credentials file somewhere?   Or maybe I'm missing something and there's a completely different solution. Can anyone help? I have been developing a few python addins and I'm just wondering what is the best way to re-compile the addin anytime I edit the script.  Currently, if I make an edit to the script, it seems like I have to   Close ArcMap Go to My addin folder and double click the 'makeaddin' python file Double click the 'Python Addin File Restart ArcMap for the changes to come into effect   If I don't do these steps, then the edits aren't recognized. This gets pretty annoying and time consuming when I want to place maybe a simple print line somewhere or I do a small edit just to test a result.  Is there a better way of doing this? Does $\pi$ contain all possible number combinations? How to calculate $\lim \limits_{n \to \infty}(1 +\frac{a}{n})^n$? Does the verb &quot;provide&quot; always have to be used with &quot;with&quot;? For example,  Can you provide me with some good examples? Can you provide me some good examples? Can you provide some good examples?  I suppose it's a transitive verb, isn't it? Moreover, is the following type of usage correct?  You should provide food for your dog before you go on vacation.  If you could give me some good examples regarding &quot;provide&quot; with different types of usage, I'd appreciate that. What is the meaning of “runneth” in ? Why is fundamental group insufficient to classify manifolds? I have heard that some issues in group theory prevent classifying all manifolds upto homotopy using the fundamental group invariant. Does anyone know what are those issues?  Thanks, K. Standard definition of graph says that it is an ordered pair G=(N,L) where N is set of nodes and L is set of lines which connect the nodes.   From what I've read, the set L can be empty, but can set N be empty too?  I'm mainly asking this because for my exam, I found numerous problems that go like this: Graph X is given. How many subgraphs with property Y exist? Often the number depends on the definition of graph. As a  developer I'm used to running through constructors:    class Test {     public Test() {         DoSomething();     }      public Test(int count) : this() {         DoSomethingWithCount(count);     }      public Test(int count, string name) : this(count) {         DoSomethingWithName(name);     } }   Is there a way to do this in C++?  I tried calling the Class name and using the 'this' keyword, but both fail. Does C1 code coverage analysis exist for Ruby? I'm currently using  to get C0 code coverage analysis for a rails project that I'm working on.  However, those results are practically meaningless- I have 100% coverage according to rcov (as it only covers C0 analysis) and I've barely written half the test cases for the functionality that exists thus far.  I'm used to the useful results from the code coverage in Visual Studio 2008 Team, which has C1 coverage.  Are there any tools that provide similar coverage for ruby? At what moment will matter falling into a black hole affect its size? Does the mass of matter falling into a black hole affect the size of an event horizon the moment it passes through it, or when it has been incorporated into the singularity? Parsing JSON from URL Cut strokes from other shapes via pathfinder How far can I refactor the code in someone else's question? What space does the spell Cloud of Daggers fill? I am trying to workout what template  (PHB, p. 222) would be on a grid. The spell states:     You fill the air with spinning daggers in a cube 5 feet on each side, centered on a point you choose within range.   So does that mean it would look like this:     Or like this:    From what I've read online, there seems to be some suggestion that it is a single square (tile) though this does stack with the spell description of "a cube 5 feet on each side".  Clearing this up for my group would be great, and I am sure our DM will be pleased as his monster were nicely diced by this spell. Thanks. If column matches another file, print every line with match (awk/grep) I’m taking two input files, one with certain ID numbers, and another with a large list of ID numbers and additional columns. The latter file contains multiple lines for each ID number and I need to extract all lines that match an ID from the first file. Those lines then must be printed in a new file.  Edit 1: Replaced sample files with excerpts from actual  Edit 2: Removed extra spaces that were in excerpt, but not actual file. Files likely need to be sanitized in some way, but how is unclear.  file1:  AT1G56430 AT3G55190 AT3G22880   file2:  AT1G01010|GO:0043090|RCA AT1G56430|GO:0010233|IGI  AT1G56430|GO:0009555|IGI  AT1G56430|GO:0030418|IGI   expected output  AT1G56430|GO:0010233|IGI  AT1G56430|GO:0009555|IGI  AT1G56430|GO:0030418|IGI   [[  I have tried:  awk -F'|' 'NR==FNR{c[$1$2]++;next};c[$1$2] &gt; 0' file1 file2 &gt; output.txt   and:  grep -Ff file2 file1 &gt; output.txt   I’m aware that there are many somewhat similar questions posted in these forums and others. However, these don’t mention how the output is handled… nor do they mention duplicates. I’ve tried solutions from 4 of them, have been messing with this for many hours and keep getting the same problem: a blank output file.   I’m new to awk and I greatly appreciate the help. Sorry if this is a simple problem with syntax etc; please let me know. Thanks for the help. I got to read Volume I of Feynmann's lectures. It said that at absolute zero, molecular motion doesn't cease at all, because if that happens, we will be able to make precise determination of position and momentum of the atom. We do know that Heisenberg uncertainty principle holds for microscopic particles in motion. But what then is wrong to consider that all molecular motion ceases at absolute zero? In other words, does the uncertainty principle not hold when there is no motion?  Need some help! window.onbeforeunload and window.onunload is not working in Firefox, Safari, Opera?