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	<title>Real-Time Physics Simulation Forum</title>
	
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	<updated>2018-04-05T04:36:38+00:00</updated>

	<author><name><![CDATA[Real-Time Physics Simulation Forum]]></name></author>
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		<entry>
		<author><name><![CDATA[coderchris]]></name></author>
		<updated>2018-04-05T04:36:38+00:00</updated>

		<published>2018-04-05T04:36:38+00:00</published>
		<id>https://pybullet.org/Bullet/phpBB3/viewtopic.php?p=40536#p40536</id>
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		<title type="html"><![CDATA[Geometric stiffness term in Stable Constrained Dynamics]]></title>

		
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This is in reference to "Stable Constrained Dynamics": <a href="https://hal.inria.fr/hal-01157835/document" class="postlink">https://hal.inria.fr/hal-01157835/document</a><br><br>Equation (18) / (21)<br><br>I'm having trouble understanding how to build this K "geometric stiffness" term.<br><br>K = (∂J^T / ∂x) λ<br><br>Where J is the constraints jacobian and λ is the constraint force magnitudes.<br><br>What I do know - based on its usage in (21), K should be a (3n x 3n) matrix in 3D where n is the number of particles lets say.<br><br>What I'm confused about - the jacobian J is a (C x 3n) matrix where C is the number of constraints. λ is (C x 1). This doesn't seem to work out in terms of the matrix dimensions...<br><br>What am I missing here?<br><br>If I consider only a single constraint, then it does appear to work out in terms of the dimensions - I end up with λ being a scalar and K ultimately being (3n x 3n). However, that leads to the question of how to then build K such that it contains all of the individual constraint K's (one K for each constraint I guess)?<p>Statistics: Posted by <a href="https://pybullet.org/Bullet/phpBB3/memberlist.php?mode=viewprofile&amp;u=743">coderchris</a> — Thu Apr 05, 2018 4:36 am</p><hr />
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