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	<title>Sciduck</title>
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		<title>How Liking Zombies is like Being Interested in Medicine</title>
		<link>http://www.sciduck.com/sciduck/how-liking-zombies-is-like-being-interested-in-medicine/</link>
		<comments>http://www.sciduck.com/sciduck/how-liking-zombies-is-like-being-interested-in-medicine/#comments</comments>
		<pubDate>Wed, 30 Nov 2011 06:11:17 +0000</pubDate>
		<dc:creator>Sienna</dc:creator>
				<category><![CDATA[science/math]]></category>
		<category><![CDATA[education]]></category>
		<category><![CDATA[medicine]]></category>
		<category><![CDATA[zombies]]></category>

		<guid isPermaLink="false">http://www.sciduck.com/?p=398</guid>
		<description><![CDATA[Hiya Sciducks, It may be that you, like Kevin, don&#8217;t quite believe in medicine as much as you believe in The Impending Zombie Apocalypse. You aren&#8217;t worried that one day you will be on medications for heart failure, type II diabetes, hypertension, and probably a couple of other things for self-diagnosed sleep problems plus or <a href='http://www.sciduck.com/sciduck/how-liking-zombies-is-like-being-interested-in-medicine/'>[...]</a>]]></description>
			<content:encoded><![CDATA[<p>Hiya Sciducks,</p>
<p>It may be that you, like Kevin, don&#8217;t quite believe in medicine as much as you believe in The Impending Zombie Apocalypse. You aren&#8217;t worried that one day you will be on medications for heart failure, type II diabetes, hypertension, and probably a couple of other things for self-diagnosed sleep problems plus or minus a mood disorder or two. That&#8217;s for people who get old waiting for the Zombie Apocalypse.</p>
<p>In the event that the known world becomes a hunting ground for the Undead, I will agree with you that medical knowledge is probably about as useful as you are after twenty White Walkers have descended to feast on your flesh (Sorry, am I mixing fandoms? <em>Winter is coming!</em>). But for the moment, let us attempt a thought experiment and say: One, that medicine might be relevant to our lives, and two, that it might be interesting.<span id="more-398"></span></p>
<p>I mean, if you like zombies &#8211; you like gory, gross, weird, infectious stuff; you&#8217;re on the cusp of liking medicine. When the interviewers asked me why I wanted to go to medical school, I was tempted to tell them the actual truth, which was that I read <em>The Hot Zone </em>in 6th grade and never got over it &#8211; and by it I mean, that feeling where you can&#8217;t look away from something, even when you know it&#8217;s gone horribly wrong.  (On that subject, some Google-image searches that I don&#8217;t recommend include: <strong>harlequin&#8217;s ichythiosis </strong>&amp; <strong>Stevens-Johnson Syndrome. </strong> Yes. You are welcome.)</p>
<p>But we are getting ahead of ourselves.</p>
<p>Hi. I&#8217;m Sienna, a second year med student. I attend one of the schools on the Continental United States (which, as it happens, <em>was</em> my articulated goal in undergrad. I know. Ambitious). Second year med school means that instead of cramming for the exam two days before, you start a full week ahead. A full week might not sound like cramming to you, but that’s what we med students are: rule-breakers. We chip away at the boundaries of truth, we blur the line between over-preparation and last-minute cramming. We are so cool.</p>
<p>Being a second year also means that I am a complete idiot, with some medical knowledge. Say you told me you feel tired and had a nosebleed yesterday. Diagnosis? Acute Lymphoblastic Leukemia. Left hand feeling a little numb? Transient Ischemic Attack! Or maybe it&#8217;s tertiary syphilis (had sex with anyone weird like&#8230;25 years ago?). Headache? It&#8217;s probably a subarachnoid hemorrhage. Or maybe it&#8217;s diabetes.  So this is the only serious thing I probably will ever say: I advise strongly against seeking medical advice from yours truly.</p>
<p>Not that I will offer you any. Besides, the Zombies will probably get to you first.</p>
<p>So I&#8217;ve basically said next to nothing, except &#8220;hi&#8221;  in the most roundabout and digressive way imaginable. When I do, eventually, get to some real content, I will probably report back about weird things I learn in and out of school. At the moment we are covering -</p>
<p>Drum roll please -</p>
<p>Psych problems. Let&#8217;s start by talking about melancholia, internet.</p>
<p>Cheers.</p>
<p>S</p>
]]></content:encoded>
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		<title>Sciduck Relaunch</title>
		<link>http://www.sciduck.com/news/sciduck-relaunch/</link>
		<comments>http://www.sciduck.com/news/sciduck-relaunch/#comments</comments>
		<pubDate>Mon, 10 Oct 2011 05:22:42 +0000</pubDate>
		<dc:creator>kevin</dc:creator>
				<category><![CDATA[site news]]></category>
		<category><![CDATA[launch]]></category>
		<category><![CDATA[reboot]]></category>

		<guid isPermaLink="false">http://www.sciduck.com/?p=383</guid>
		<description><![CDATA[We promise this will be just as bad as your favorite movie reboot.  Get ready!]]></description>
			<content:encoded><![CDATA[<p>We promise this will be just as bad as your favorite movie reboot.  Get ready!</p>
]]></content:encoded>
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		<title>Nintendo&#8217;s Mistakes Led To Their Eventual Success.</title>
		<link>http://www.sciduck.com/tech/nintendos-mistakes-led-to-their-eventual-success/</link>
		<comments>http://www.sciduck.com/tech/nintendos-mistakes-led-to-their-eventual-success/#comments</comments>
		<pubDate>Sat, 20 Mar 2010 21:50:03 +0000</pubDate>
		<dc:creator>Jon</dc:creator>
				<category><![CDATA[technology]]></category>
		<category><![CDATA[Gaming]]></category>
		<category><![CDATA[nintendo]]></category>

		<guid isPermaLink="false">http://www.sciduck.com/?p=355</guid>
		<description><![CDATA[Currently Nintendo are winning the console war with close to 70 million Wii consoles sold worldwide, however this was not always the case. Infact over the last 10 years Nintendo home consoles have failed to make a huge impact with the N64 and Gamecube being comparative flops when compared to the success of the Playstation, <a href='http://www.sciduck.com/tech/nintendos-mistakes-led-to-their-eventual-success/'>[...]</a>]]></description>
			<content:encoded><![CDATA[<p style="text-align: center;"><img class="aligncenter" title="Nintendo" src="http://pulse2.com/wp-content/uploads/2009/05/nintendo-logo.png" alt="" width="463" height="114" /></p>
<p>Currently <a href="http://en.wikipedia.org/wiki/Nintendo">Nintendo</a> are winning the console war with close to 70 million <a href="http://en.wikipedia.org/wiki/Wii">Wii</a> consoles sold worldwide, however this was not always the case. Infact over the last 10 years Nintendo home consoles have failed to make a huge impact with the <a href="http://en.wikipedia.org/wiki/Nintendo_64">N64 </a>and <a href="http://en.wikipedia.org/wiki/Nintendo_GameCube">Gamecube</a> being comparative flops when compared to the success of the <a href="http://en.wikipedia.org/wiki/Playstation">Playstation</a>, <a href="http://en.wikipedia.org/wiki/Playstation2">Playstation 2</a> and the <a href="http://en.wikipedia.org/wiki/Xbox">Xbox</a>. The mistakes Nintendo made in the previous three generations of consoles were somewhat fatal to them then, however as a result of these mistakes Nintendo and their Wii console are tremendously successful. Read on to find out how Nintendo’s mistakes caused their downfall in the mid 90’s to their successes now.</p>
<p><span id="more-355"></span></p>
<div class="wp-caption alignleft" style="width: 280px"><img class=" " title="Playstation" src="http://regmedia.co.uk/2007/04/27/sony_first_playstation.jpg" alt="" width="270" height="169" /><p class="wp-caption-text">The Playstation, A Monument To Nintendo&#39;s Sins.</p></div>
<p>Now we are used to a console war between <a href="http://en.wikipedia.org/wiki/Sony">Sony</a>, Nintendo and <a href="http://en.wikipedia.org/wiki/Microsoft">Microsoft</a> this however was not always the case. In the early 1990’s Nintendo and <a href="http://en.wikipedia.org/wiki/Sega">Sega</a> with their <a href="http://en.wikipedia.org/wiki/Snes">SNES </a>and <a href="http://en.wikipedia.org/wiki/Megadrive">Mega Drive</a> respectively were the leaders in the console war. While the SNES was very successful for Nintendo a key decision made by Nintendo changed the gaming industry forever. In the late 80’s Nintendo formed a partnership with Sony to produce a disc drive for the <a href="http://en.wikipedia.org/wiki/Nintendo_Entertainment_System">Famicom (NES)</a> and later the SNES, however when Nintendo felt that the terms of the contract were unfair as it would give Sony creative control of all the projects using the disc drive system Nintendo cancelled the project. Sony however continued to develop the technology, which would later become the Playstation and go on to sell over 100 million units compared to its main rival the N64 which sold 33 million units.</p>
<div class="wp-caption alignright" style="width: 250px"><img class=" " title="N64" src="http://www.playoldgames.net/stories/game_boxes/oot_cart.jpg" alt="" width="240" height="161" /><p class="wp-caption-text">The Technically Limited N64 Cartridge.</p></div>
<p>The Nintendo 64 itself caused problems for Nintendo, the decision to use outdated cartridges to avoid piracy which was common with disc media, was a problem for many developers as it was more expensive to produce and buy causing developers to be hesitant to develop for the N64 due to the higher production costs. Furthermore the low texture cache of 4KB caused problems with limitations on what developers could achieve, as a result many N64 games suffered from poor blurry textures when compared to the Playstation. However the biggest problem the N64 suffered from in my opinion was the limited space on the cartridge (64MB) when compared to the disc media of the Playstation, as a result many franchises that had been synonymous with Nintendo soon shifted onto the Playstation where they would go on to become hugely successful and fuel console sales, in particular this includes<a href="http://en.wikipedia.org/wiki/Ff7"> Final Fantasy 7</a> and the <a href="http://en.wikipedia.org/wiki/Metal_Gear_(series)">Metal Gear franchise</a>.</p>
<div class="wp-caption alignleft" style="width: 250px"><img class=" " title="Gamecube Disc." src="http://img.hexus.net/v2/gaming/gamecube/gcn05.jpg" alt="" width="240" height="180" /><p class="wp-caption-text">Gamecube DVD and Standard DVD Comparison.</p></div>
<p>In November 2001 the Nintendo Gamecube was released to moderate success. Initially the console went second in the console war ahead of the fledgling Xbox but far behind the established Playstation 2, by the end of the generation the Gamecube however was firmly in last place. This is in my opinion heavily due to Nintendo’s decision to use a mini-DVD as the choice of media when compared to the standard DVD’s that both the PS2 and Xbox used, Nintendo again concerned with piracy made the decision to use a heavily limited media with only 1.5GB of available disc space when compared with the 4.7GB available to the PS2 and Xbox, as a result despite being more powerful than the PS2 many multiplatform games were limited due to the disc space. Key examples this were <a href="http://en.wikipedia.org/wiki/Timesplitters_2">Timesplitters 2</a> and the <a href="http://en.wikipedia.org/wiki/Ea_sports">EA Sports</a> series which managed to include much more content onto the multiplatform versions when compared to the Gamecube.</p>
<p>The failure of the Gamecube lead to Nintendo’s decision to develop a gaming system unlike any other around and the result was the Wii, which utilised motion controls. However while successful I feel that Nintendo did miss a trick with the Wii, when first announced the <a href="http://en.wikipedia.org/wiki/Wii_Remote">motion controls</a> were very limited before being upgraded to the <a href="http://en.wikipedia.org/wiki/Wii_MotionPlus">Wii Motion Plus </a>last year, furthermore the reluctance of Nintendo to try and compete with the HD Generation of games has lead to criticism that the Wii is a glorified Gamecube which is partially true, when the motion controls were first demonstrated in the Metroid Prime Tech Demo, it was actually played on a Gamecube retrofitted with Motion controls. I feel that the Wii has suffered in recent years due to its reluctance to embrace HD as more gamers have now started to turn to the <a href="http://en.wikipedia.org/wiki/Xbox_360">Xbox 360</a> and <a href="http://en.wikipedia.org/wiki/Ps3">PS3</a> after using a Wii and getting bored of what it offers.</p>
<p>Furthermore Nintendo’s dominance of the handheld format has also lead to laziness in their development of a new console, the original <a href="http://en.wikipedia.org/wiki/Gameboy">Gameboy</a> was released in 1989 and it wasn’t until 12 years later we got a true successor with the <a href="http://en.wikipedia.org/wiki/Gameboy_advance">Gameboy Advance</a>, however in that 12 years we have the Gameboy Pocket and Gameboy Colour redesigns that did nothing to really advance the technology. This attitude of redesigning handhelds carried over to both the Gameboy Advance with GBA SP and GBA Micro and the <a href="http://en.wikipedia.org/wiki/Nintendo_ds">Nintendo DS</a> with the DS Lite, DSi and DSi XL <a href="http://en.wikipedia.org/wiki/Nintendo_ds#Redesigns">redesigns</a>. As a result of this dominance I feel Nintendo are more inclined to redesign consoles rather then develop the technology. A similar attitude can in my opinion be seen in Nintendo’s software design.</p>
<div class="wp-caption alignnone" style="width: 640px"><a href="http://thepointofitall.files.wordpress.com/2009/04/gameboy-timeline-hd2.jpg" title="Nintendo Handhelds." rel="lightbox[355]"><img class="   " title="Nintendo Handhelds." src="http://thepointofitall.files.wordpress.com/2009/04/gameboy-timeline-hd2.jpg" alt="" width="630" height="267" /></a><p class="wp-caption-text">Redesign over Revolution?</p></div>
<p> </p>
<div class="wp-caption alignright" style="width: 136px"><img class="   " title="Fludd." src="http://themushroomkingdom.net/images/sms/sms_mario_fludd.jpg" alt="" width="126" height="191" /><p class="wp-caption-text">F.L.U.D.D. More Gimmick Than Gold.</p></div>
<p>The <a href="mariowiki.com/">Mario</a> Series, spanning over 20 years since its debut has always followed a similar formula even after shifting into 3D, the premise of you having to save a kidnapped Princess. Even after shifting into 3D with <a href="http://www.mariowiki.com/Super_Mario_64">Mario 64 </a>this premise remained the same, however instead of progressing through worlds you had to gain power stars before saving her from Bowser. Even the New Super Mario Bros Wii has followed the format from 20 years ago of progressing through worlds while adding little to the core gameplay, <a href="http://www.mariowiki.com/Super_Mario_Sunshine">Super Mario Sunshine</a> and <a href="http://www.mariowiki.com/Super_Mario_Galaxy">Mario Galaxy</a> are examples of this with the FLUDD device in Sunshine and the idea of traversing planets in Galaxy being added while being little more than a gimmick.</p>
<p>Like the Mario Series, <a href="http://www.zeldawiki.org/Main_Page">Zelda</a> has at its core remained the same even after a shift into 3D with a overworld with dungeons connected which you must complete to advance being favoured. Very little has been added aside from some new weapons or enemies but the premise remains the same, the latest in the series <a href="http://www.zeldawiki.org/The_Legend_of_Zelda:_Twilight_Princess">Twilight Princess </a>is heavily influence by previous titles; in particular <a href="http://www.zeldawiki.org/The_Legend_of_Zelda:_Ocarina_of_Time">Ocarina Of Time</a> with some bosses being identical and this is a sure sign of the series becoming stale, however Nintendo has promised that the <a href="http://www.zeldawiki.org/Zelda_Wii">next in the series</a> will shift away from this format.</p>
<div class="wp-caption alignleft" style="width: 234px"><img class=" " title="Pokemon" src="http://www.foxnews.com/images/282525/0_61_pokemon_pearl.jpg" alt="" width="224" height="168" /><p class="wp-caption-text">Pokémon Pearl. Good Graphics But Not Great.</p></div>
<p><a href="http://pokemon.wikia.com/wiki/Pokémon_Wiki">Pokémon</a> has been a staple of the Nintendo’s handheld systems since its initial release in Japan 15 years ago, however over this time the dynamic has not really changed. While <a href="http://pokemon.wikia.com/wiki/Pokémon_Gold_and_Silver">Gold and Silver</a> heralded a massive change in gameplay with the Day/ Night dynamic, the Pokégear and the breeding system these changes were simplified and streamlined in further instalments while not really adding much aside from new Pokémon that are beginning to recycle earlier ideas and new regions. While the graphics have improved in the games they are still nowhere near the best looking games on the Nintendo DS with a hybrid of the DS’s 3D capabilities and the trademark Pokémon style. However for years now fans have been clamouring for a fully 3D Pokémon title on a home console and while Nintendo have developed games such as <a href="http://pokemon.wikia.com/wiki/Pokémon_XD:_Gale_of_Darkness">Pokémon XD: Gale of Darkness</a> they have been reluctant to translate the franchise into a full 3D adventure. Furthermore Nintendo&#8217;s insistence to remake previous games with improved graphics shows laziness on their part.</p>
<p>The Nintendo Wii while hugely successful has been criticised for the quality of some of its games, in particular that outside of the first party titles that there is a lack of quality. However I believe that Nintendo’s decision to translate older Gamecube games into <a href="http://en.wikipedia.org/wiki/New_Play_Control">New Play ports</a> with motion controls and slightly improved graphics shows laziness and complacency that has resulted from the success of the Wii rather than a desire to build fresh new franchises.</p>
<div class="wp-caption aligncenter" style="width: 437px"><img class=" " title="Wii HD" src="http://videogame2play.com/wp-content/uploads/2009/10/codreflexsidebyside2.jpg" alt="" width="427" height="255" /><p class="wp-caption-text">The Wii, Failing To Embrace HD.</p></div>
<p> </p>
<p>In conclusion while Nintendo have been lazy it has lead to success by going against the grain with Motion Controls with the Wii, however they would never have found themselves in this position had they not abandoned Sony’s ideas for a disc system which would later go on to be developed as the Playstation. The insistence to rely on cartridges rather than CD’s lead to ground being lost by the N64 which was further lost by the Gamecube and the lack of AAA titles and the use of Mini-DVD which had a very restricted memory. Now that Nintendo are back in pole position I hope that complacency does not set in and I still feel that by disregarding the HD generation Nintendo are missing a trick, only time will tell.</p>
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		</item>
		<item>
		<title>Happy Birthday Jon!</title>
		<link>http://www.sciduck.com/uncategorized/happy-birthday-jon/</link>
		<comments>http://www.sciduck.com/uncategorized/happy-birthday-jon/#comments</comments>
		<pubDate>Wed, 17 Mar 2010 01:32:18 +0000</pubDate>
		<dc:creator>kevin</dc:creator>
				<category><![CDATA[Uncategorized]]></category>

		<guid isPermaLink="false">http://www.sciduck.com/?p=350</guid>
		<description><![CDATA[Happy birthday to Jon!]]></description>
			<content:encoded><![CDATA[<h1 style="text-align: center;"><span style="color: #00ffff;"><strong>Happy birthday to Jon! </strong></span></h1>
<p><span style="color: #00ffff;"><strong><br />
</strong></span></p>
<p style="text-align: center;"><object classid="clsid:d27cdb6e-ae6d-11cf-96b8-444553540000" width="425" height="350" codebase="http://download.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,40,0"><param name="src" value="http://www.youtube.com/v/XLBaOlc-zzQ" /><embed type="application/x-shockwave-flash" width="425" height="350" src="http://www.youtube.com/v/XLBaOlc-zzQ"></embed></object></p>
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		</item>
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		<title>Basic Control Analysis</title>
		<link>http://www.sciduck.com/sciduck/basic-control-analysis/</link>
		<comments>http://www.sciduck.com/sciduck/basic-control-analysis/#comments</comments>
		<pubDate>Tue, 16 Mar 2010 02:35:25 +0000</pubDate>
		<dc:creator>kevin</dc:creator>
				<category><![CDATA[science/math]]></category>
		<category><![CDATA[controls]]></category>
		<category><![CDATA[electrical engineering]]></category>
		<category><![CDATA[math]]></category>

		<guid isPermaLink="false">http://www.sciduck.com/?p=299</guid>
		<description><![CDATA[Controls has become one of the biggest (and most important) areas in electrical engineering.  However, many times when implementing a controls solution, we need to work with linear systems.  The majority of real life systems are not linear! So how do we fix this? With linearization.  In this article I&#8217;ll walk you through an example <a href='http://www.sciduck.com/sciduck/basic-control-analysis/'>[...]</a>]]></description>
			<content:encoded><![CDATA[<p>Controls has become one of the biggest (and <a href="http://www.evolvingexcellence.com/blog/2009/09/toyotas-inexcusable-failure.html">most important</a>) areas in electrical engineering.  However, many times when implementing a controls solution, we need to work with linear systems.  The majority of real life systems are <strong>not </strong>linear! So how do we fix this? With linearization.  In this article I&#8217;ll walk you through an example of how to linearize a system around a certain state vector and control input!</p>
<p style="text-align: center;">
<div id="attachment_327" class="wp-caption aligncenter" style="width: 310px"><a href="http://www.sciduck.com/wp-content/uploads/2010/03/basic.jpg" title="Example control system" rel="lightbox[299]"><img class="size-medium wp-image-327 " style="border: 2px solid white;" title="Example control system" src="http://www.sciduck.com/wp-content/uploads/2010/03/basic-300x157.jpg" alt="Example control system" width="300" height="157" /></a><p class="wp-caption-text">Example control system</p></div>
<p><span id="more-299"></span></p>
<p>Okay so let&#8217;s say your system (ie, the thing you want to control) is modeled by the following differential equation (y is the output, u is the input):</p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=%5Cfrac%7Bd%5E2%20y%7D%7Bdt%5E2%7D%2B4%20%5Cfrac%7Bdy%7D%7Bdt%7D%20%2B%20%28y%5E2%20-%201%29%20%5Ccdot%20u%20%3D%200&#038;bg=000000&#038;fg=ffffff&#038;s=2' alt='\frac{d^2 y}{dt^2}+4 \frac{dy}{dt} + (y^2 - 1) \cdot u = 0' title='\frac{d^2 y}{dt^2}+4 \frac{dy}{dt} + (y^2 - 1) \cdot u = 0' class='latex' /></p>
<p style="text-align: left;">Say we want to linearize around the state vector x = 0, and the input u = 0. We&#8217;re going to need to represent this system in state space form, so let&#8217;s do it.</p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=x_1%20%3D%20y&#038;bg=000000&#038;fg=ffffff&#038;s=2' alt='x_1 = y' title='x_1 = y' class='latex' /></p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=x_2%20%3D%20%5Cdot%20y&#038;bg=000000&#038;fg=ffffff&#038;s=2' alt='x_2 = \dot y' title='x_2 = \dot y' class='latex' /></p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=%5Cdot%20x_1%20%3D%20x_2&#038;bg=000000&#038;fg=ffffff&#038;s=2' alt='\dot x_1 = x_2' title='\dot x_1 = x_2' class='latex' /></p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=%5Cdot%20x_2%20%3D%20-4%20x_2%20-%20%28x_1%20%5E2%20-%201%29%20%5Ccdot%20u&#038;bg=000000&#038;fg=ffffff&#038;s=2' alt='\dot x_2 = -4 x_2 - (x_1 ^2 - 1) \cdot u' title='\dot x_2 = -4 x_2 - (x_1 ^2 - 1) \cdot u' class='latex' /></p>
<p style="text-align: left;">That wasn&#8217;t too bad, state space is great.  Now we can see it clearly isn&#8217;t linear, there is a squared term~~!  So the first step to linearization requires us to find the <a href="http://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant">Jacobian</a> matrices.  Let&#8217;s do it.</p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=%20A%20%3D%20%5Cbegin%7Bbmatrix%7D%20%5Cfrac%7B%5Cpartial%20f_1%7D%7B%5Cpartial%20x_1%7D%20%26%20%5Cfrac%7B%5Cpartial%20f_1%7D%7B%5Cpartial%20x_2%7D%20%5C%5C%5Cfrac%7B%5Cpartial%20f_2%7D%7B%5Cpartial%20x_1%7D%20%26%20%5Cfrac%7B%5Cpartial%20f_2%7D%7B%5Cpartial%20x_2%7D%20%5Cend%7Bbmatrix%7D&#038;bg=000000&#038;fg=ffffff&#038;s=2' alt=' A = \begin{bmatrix} \frac{\partial f_1}{\partial x_1} &amp; \frac{\partial f_1}{\partial x_2} \\\frac{\partial f_2}{\partial x_1} &amp; \frac{\partial f_2}{\partial x_2} \end{bmatrix}' title=' A = \begin{bmatrix} \frac{\partial f_1}{\partial x_1} &amp; \frac{\partial f_1}{\partial x_2} \\\frac{\partial f_2}{\partial x_1} &amp; \frac{\partial f_2}{\partial x_2} \end{bmatrix}' class='latex' /></p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=%20A%20%3D%20%5Cbegin%7Bbmatrix%7D%200%20%26%201%20%5C%5C%5C%200%20%26%20-4%20%5Cend%7Bbmatrix%7D&#038;bg=000000&#038;fg=ffffff&#038;s=2' alt=' A = \begin{bmatrix} 0 &amp; 1 \\\ 0 &amp; -4 \end{bmatrix}' title=' A = \begin{bmatrix} 0 &amp; 1 \\\ 0 &amp; -4 \end{bmatrix}' class='latex' /></p>
<p style="text-align: left;">Similarly, we want to take partial derivatives for the input, in control systems, we call this the B matrix:</p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=B%20%3D%20%5Cbegin%7Bbmatrix%7D%5Cfrac%7B%5Cpartial%20f_1%7D%7B%5Cpartial%20u%7D%20%5C%5C%20%5Cfrac%7B%5Cpartial%20f_2%7D%7B%5Cpartial%20u%7D%20%5Cend%7Bbmatrix%7D&#038;bg=000000&#038;fg=ffffff&#038;s=2' alt='B = \begin{bmatrix}\frac{\partial f_1}{\partial u} \\ \frac{\partial f_2}{\partial u} \end{bmatrix}' title='B = \begin{bmatrix}\frac{\partial f_1}{\partial u} \\ \frac{\partial f_2}{\partial u} \end{bmatrix}' class='latex' /></p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=B%20%3D%20%5Cbegin%7Bbmatrix%7D%200%20%5C%5C%201%20%5Cend%7Bbmatrix%7D&#038;bg=000000&#038;fg=ffffff&#038;s=2' alt='B = \begin{bmatrix} 0 \\ 1 \end{bmatrix}' title='B = \begin{bmatrix} 0 \\ 1 \end{bmatrix}' class='latex' /></p>
<p style="text-align: left;">Standard state space representation tells us now, that we basically have linearized our system!  You can see this clearly by representing the system in state space form.</p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=%5Cbegin%7Bbmatrix%7D%5Cdot%20x_1%20%5C%5C%20%5Cdot%20x_2%5Cend%7Bbmatrix%7D%20%3D%20A%20%5Cbegin%7Bbmatrix%7D%20x_1%20%5C%5C%20x_2%20%5Cend%7Bbmatrix%7D%2B%20B%20u&#038;bg=000000&#038;fg=ffffff&#038;s=2' alt='\begin{bmatrix}\dot x_1 \\ \dot x_2\end{bmatrix} = A \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}+ B u' title='\begin{bmatrix}\dot x_1 \\ \dot x_2\end{bmatrix} = A \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}+ B u' class='latex' /></p>
<p style="text-align: left;">Realizing the vectors are just representations for x1 and x2, we now have the following system of equations:</p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=%5Cdot%20x_1%20%3D%20x_2&#038;bg=000000&#038;fg=ffffff&#038;s=2' alt='\dot x_1 = x_2' title='\dot x_1 = x_2' class='latex' /></p>
<p style="text-align: center;"><img src='http://s.wordpress.com/latex.php?latex=%5Cdot%20x_2%20%3D%20-4%20x_2%20%2B%20u&#038;bg=000000&#038;fg=ffffff&#038;s=2' alt='\dot x_2 = -4 x_2 + u' title='\dot x_2 = -4 x_2 + u' class='latex' /></p>
<p style="text-align: left;">Clearly a linear system.  So in summation, to linearize a non linear system, it is quite simple.  Represent the system in state space form.  Then find the jacobian matrices, and evaluate around the point(s) you want to linearize around.  Then you are done!  Later (read: when I don&#8217;t have interviews), I will show how we can use this to model a maglev system.</p>
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