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	<title>Comments on: MIT-developed ion &#8216;microthrusters&#8217; could propel small satellites</title>
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	<link>http://www.kurzweilai.net/mit-developed-ion-microthrusters-could-propel-small-satellites</link>
	<description>Accelerating Intelligence</description>
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		<title>By: Hugh</title>
		<link>http://www.kurzweilai.net/mit-developed-ion-microthrusters-could-propel-small-satellites/comment-page-1#comment-28854</link>
		<dc:creator>Hugh</dc:creator>
		<pubDate>Mon, 20 Aug 2012 04:50:28 +0000</pubDate>
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		<description>I knew that!</description>
		<content:encoded><![CDATA[<p>I knew that!</p>
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		<title>By: Alastair Carnegie</title>
		<link>http://www.kurzweilai.net/mit-developed-ion-microthrusters-could-propel-small-satellites/comment-page-1#comment-28817</link>
		<dc:creator>Alastair Carnegie</dc:creator>
		<pubDate>Sun, 19 Aug 2012 19:05:37 +0000</pubDate>
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		<description>&quot;The Wronskian and linear independance&quot; (Wikipedia)
A common misconception is that W = 0 everywhere implies linear dependence, but Peano (1889) pointed out that the functions x2 and &#124;x&#124;x have continuous derivatives and their Wronskian vanishes everywhere, yet they are not linearly dependent in any neighborhood of 0. There are several extra conditions which ensure that the vanishing of the Wronskian in an interval implies linear dependence. Peano (1889) observed that if the functions are analytic, then the vanishing of the Wronskian in an interval implies that they are linearly dependent. Bochner (1901) gave several other conditions for the vanishing of the Wronskian to imply linear dependence; for example, if the Wronskian of n functions is identically zero and the n Wronskians of n–1 of them do not all vanish at any point then the functions are linearly dependent. Wolsson (1989a) gave a more general condition that together with the vanishing of the Wronskian implies linear dependence.

Oops!  repeated roots fall into this category, and although Lagrangian mechanics is useful and reliable in most circumstances, the Russian Academy of Sciences have at last published some excellent old B&amp;W film footage of &#039;clockwork&#039; inertial drive systems. Disallowed by the convenient &#039;circulus in probando&#039; argument presented in Lagrangian Mechanics. The demonstations conclusively prove that there is not always an equal and opposite reaction, especially if we are dealing with the forces of centripetal acceleration. Very handy for manoevering Soviet Military Satellites, so Russia&#039;s recent publication into the Public Domain, is an exceptionally generous gift to the scientific community.</description>
		<content:encoded><![CDATA[<p>&#8220;The Wronskian and linear independance&#8221; (Wikipedia)<br />
A common misconception is that W = 0 everywhere implies linear dependence, but Peano (1889) pointed out that the functions x2 and |x|x have continuous derivatives and their Wronskian vanishes everywhere, yet they are not linearly dependent in any neighborhood of 0. There are several extra conditions which ensure that the vanishing of the Wronskian in an interval implies linear dependence. Peano (1889) observed that if the functions are analytic, then the vanishing of the Wronskian in an interval implies that they are linearly dependent. Bochner (1901) gave several other conditions for the vanishing of the Wronskian to imply linear dependence; for example, if the Wronskian of n functions is identically zero and the n Wronskians of n–1 of them do not all vanish at any point then the functions are linearly dependent. Wolsson (1989a) gave a more general condition that together with the vanishing of the Wronskian implies linear dependence.</p>
<p>Oops!  repeated roots fall into this category, and although Lagrangian mechanics is useful and reliable in most circumstances, the Russian Academy of Sciences have at last published some excellent old B&amp;W film footage of &#8216;clockwork&#8217; inertial drive systems. Disallowed by the convenient &#8216;circulus in probando&#8217; argument presented in Lagrangian Mechanics. The demonstations conclusively prove that there is not always an equal and opposite reaction, especially if we are dealing with the forces of centripetal acceleration. Very handy for manoevering Soviet Military Satellites, so Russia&#8217;s recent publication into the Public Domain, is an exceptionally generous gift to the scientific community.</p>
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		<title>By: Bri</title>
		<link>http://www.kurzweilai.net/mit-developed-ion-microthrusters-could-propel-small-satellites/comment-page-1#comment-28705</link>
		<dc:creator>Bri</dc:creator>
		<pubDate>Sat, 18 Aug 2012 19:14:53 +0000</pubDate>
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		<description>I like the idea of a micro mirror, but instead use it to divert sunlight from over heating the earth. It could in theory make cooler areas warmer and warmer areas cooler. With a far better understanding of atmospheric science, it could even take the punch out of a hurricane.</description>
		<content:encoded><![CDATA[<p>I like the idea of a micro mirror, but instead use it to divert sunlight from over heating the earth. It could in theory make cooler areas warmer and warmer areas cooler. With a far better understanding of atmospheric science, it could even take the punch out of a hurricane.</p>
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		<title>By: asiwel</title>
		<link>http://www.kurzweilai.net/mit-developed-ion-microthrusters-could-propel-small-satellites/comment-page-1#comment-28703</link>
		<dc:creator>asiwel</dc:creator>
		<pubDate>Sat, 18 Aug 2012 18:51:54 +0000</pubDate>
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		<description>Just wondering, if this microthruster design could be paired with the Texas Instruments chip sized array of micro-mirrors as deflectors (or some other kind of electromagnetic deflector) so the ion bean or puff cloud could be controlled directionally right on the chip, at least through a small range of angles. Then maybe there would be no need to &quot;move&quot; the thruster to change the angle of thrust and go in a slightly different direction.</description>
		<content:encoded><![CDATA[<p>Just wondering, if this microthruster design could be paired with the Texas Instruments chip sized array of micro-mirrors as deflectors (or some other kind of electromagnetic deflector) so the ion bean or puff cloud could be controlled directionally right on the chip, at least through a small range of angles. Then maybe there would be no need to &#8220;move&#8221; the thruster to change the angle of thrust and go in a slightly different direction.</p>
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		<title>By: Bri</title>
		<link>http://www.kurzweilai.net/mit-developed-ion-microthrusters-could-propel-small-satellites/comment-page-1#comment-28693</link>
		<dc:creator>Bri</dc:creator>
		<pubDate>Sat, 18 Aug 2012 16:38:57 +0000</pubDate>
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		<description>These things are a godsend. Now it will be not only feasible, but affordable to clean up space trash. We are so close to critical mass, to make a cascade collision in near earth orbit. It wouldn&#039;t put us in the stone age, but it would feel like it. Once the cascade starts, there would be nothing we could do, other than watch in horror, as a big chunk of our technology, would be render useless in a matter of days.</description>
		<content:encoded><![CDATA[<p>These things are a godsend. Now it will be not only feasible, but affordable to clean up space trash. We are so close to critical mass, to make a cascade collision in near earth orbit. It wouldn&#8217;t put us in the stone age, but it would feel like it. Once the cascade starts, there would be nothing we could do, other than watch in horror, as a big chunk of our technology, would be render useless in a matter of days.</p>
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		<title>By: Howard Graves</title>
		<link>http://www.kurzweilai.net/mit-developed-ion-microthrusters-could-propel-small-satellites/comment-page-1#comment-28578</link>
		<dc:creator>Howard Graves</dc:creator>
		<pubDate>Fri, 17 Aug 2012 20:24:31 +0000</pubDate>
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		<description>I saw these at Xerox Electro-Optical Systems in 1980. Nothing new here.</description>
		<content:encoded><![CDATA[<p>I saw these at Xerox Electro-Optical Systems in 1980. Nothing new here.</p>
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		<title>By: Graham Rounce</title>
		<link>http://www.kurzweilai.net/mit-developed-ion-microthrusters-could-propel-small-satellites/comment-page-1#comment-28525</link>
		<dc:creator>Graham Rounce</dc:creator>
		<pubDate>Fri, 17 Aug 2012 14:31:30 +0000</pubDate>
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		<description>How do the ions get through the gold plate?</description>
		<content:encoded><![CDATA[<p>How do the ions get through the gold plate?</p>
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