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	Rigid body - Wikipedia, the free encyclopedia
		In physics, a rigid body is an idealisation of a solid body of finite size in which deformation is neglected.
		The configuration space of a rigid body with one point fixed is given by the underlying manifold of the rotation group SO(3).
		Two rigid bodies are said to be different (not copies) is that there is no proper rotation from one to the other.
	en.wikipedia.org /wiki/Rigid_body (761 words)

	Rigid Body Simulation Tutorial (Site not responding. Last check: 2007-11-06)
		Rigid body simulation is important in the modeling and verification of various physical systems.
		By rigid body it is meant that the bodies do not deform - they are totally stiff.
		To determine the coefficient of restitution of a contact an average of the coefficient of restitution of the two bodies involved is taken.
	www.cs.unc.edu /~ehmann/RigidTutorial (4079 words)

	Rigid body dynamics (Site not responding. Last check: 2007-11-06)
		Rigid body dynamics is the study of the mechanics of bodies that cannot be deformed, unlike elasticity.
		Mathematically, the big difference is that rigid bodies only need a finite number of parameters to describe their state or configuration, while elastic bodies need functions to describe their state - which is usually the deformation function.
		But for a large number of materials (metals, stone, hard plastics) bodies made of these materials behave very much as if they were rigid under normal conditions (low speed, low to moderate forces, small to medium size bodies).
	www.math.uiowa.edu /~dstewart/tech_rep/rbd.html (291 words)

	Rigid Body Dynamics Algorithm for Parallel Computers
		Starting with a collection of individual rigid bodies (rectangles), the equation of motion of each body is evaluated.
		As each body is independent of the others at this stage, all of the equations can be evaluated in parallel.
		The new algorithm is appropriate whenever it is desired to calculate the dynamics of a large system of rigid bodies on a parallel computer that supports fine-grained divide-and-conquer algorithms.
	www.ercim.org /publication/Ercim_News/enw42/featherstone.html (583 words)

	Trinkle's Rigid Body Dynamics
		The field of rigid body dynamic (more generally, multibody dynamics) is all about designing mathematical models and algorithms to predict the motions of bodies and the contact forces, including friction, that arise between them when.
		Roughly speaking, in rigid body dynamics, the w andz vectors represent relative accelerations and contact forces expressed in coordinate frames attached to the contact points (assumed isolated).
		Here are some papers related to rigid body dynamics simulation and design problems: theory, velocity-base time-stepping, theory and examples with torsional friction, the quasistatic problem, the design and manipulation planning with intermittent contacts.
	www.cs.rpi.edu /~trink/rigid_body_dynamics.html (1008 words)

	Jason Stewart -- Rigid Body Dynamics
		The focus is on implementing a "complete" rigid body dynamics simulator that accounts for angular momentum effects and uses a more accurate collision response than that used for Programming Assignment 2.
		An impulse is applied to one ball and its interaction with the remaining balls in the scene is simulated using rigid body dynamics.
		The current code now simulates the effects of torque on the rigid bodies, and angular momentum is included in the collision response.
	www.cs.unc.edu /~stewart/comp259/rbody.html (492 words)

	Rigid Body Dynamics
		A rigid body is similar to a system of particles in the sense that it is composed of particles.
		The main strategy in analyzing the motion of a rigid body is to split the motion into the linear motion of the CM and the angular motion of the body about its CM.
		The rigid body dynamics will serve as the building blocks for a more complex type of motion later: motion of a system of rigid bodies.
	kwon3d.com /theory/rigid.html (256 words)

	Rigid Body Simulation (Site not responding. Last check: 2007-11-06)
		Rigid body simulation tries to benefit from physics by applying physical laws in a simulator in order to simulate or animate the movement of objects as realistic as possible.
		In this course classical theory of rigid body simulation will be presented along with state of the art algorithms aiming at interactive realtime general purpose rigid body simulation.
		The theory and techniques of rigid body simulation serves as a foundation for most other topics within physical based animation and dynamic simulation.
	www.diku.dk /forskning/image/teaching/Courses/e02/RigidBodySimulation (188 words)

	Equations of motion for a rigid body
		The second of Euler’s two laws describes how the change of angular momentum of the rigid body is controlled by the moment of forces and couples applied on the body.
		The linear momentum of a body: The linear momentum of a body is assumed to be the sum of the linear momentum of its “particles”.
		Angular momentum for a rigid body: The angular momentum for a rigid body is the sum of the angular momentum for the “particles” in it.
	em-ntserver.unl.edu /negahban/em373/note19/note19.htm (1071 words)

	Rigid Body Collisions - Physics Simulation
		We now use a standard formula for the velocity of an arbitrary point on a rotating and translating rigid body to get the pre-collision velocities of the points of collision (which is the point P on each body).
		Let the vector n be normal (perpendicular) to the edge of body B that is being impacted, and pointing outward from body B. Also let the vector n be of length 1.
		Body A experiences an impulse of j n while body B experiences the equal but opposite impulse of −j n.
	www.myphysicslab.com /collision.html (2989 words)

	3.2 Rigid Body Assumption
		A rigid body may be described as a set of at least two points whose distance or distances between the points remains fixed [Gol50].
		The assumption that the two objects to be registered represent the same rigid body removes the necessity of the inclusion of shears or warping of the body in the transformation required for the matching.
		The representation of the brain as a rigid body in the MR and SPECT images may thus be sufficiently described by a set of points in 3-D space.
	www.bic.mni.mcgill.ca /users/lukban/section2_6_2.html (1005 words)

	Rigid Body Collision Response
		Position of a rigid body in space is characterized by a translation vector and a rotation.
		The placement of a rigid body is advantageously described relatively to its center of mass.
		The rigid body's linear momentum can be changed by an application of force F acting in the center of mass.
	www.cg.tuwien.ac.at /studentwork/CESCG/CESCG-2003/LKavan (4814 words)

	The Rigid Rotating Disk in Relativity
		Born rigidity: in 1909, Born proposed a Lorentz-invariant definition of "rigid body".
		If thus the concept of a RIGID BODY has no place in relativistic mechanics, it is nevertheless useful and natural to introduce the concept of a RIGID MOTION of a body.
		Or if you prefer, you can say that we have nearly rigid motion when Young's modulus is large enough, and the accelerations are gentle enough, so that infinitesimal pieces of the body are barely deformed, when viewed in the comoving frame of reference.
	math.ucr.edu /home/baez/physics/Relativity/SR/rigid_disk.html (1681 words)

	Optimal Angular Velocity Tracking with Fixed-Endpoint Rigid Body Motions
		The problem of finding a fixed-endpoint motion of a rigid body in three space with angular velocity close to a given, arbitrary vector function $\omega$ is considered.
		\leftu - \omega \right\big\}_p$ on an admissible class consisting of smooth rigid body motions on $[0,1]$ with prescribed endpoints are sought for $1\leq p\leq\infty$.
		While this moving frame must in general be obtained numerically, it can be obtained in advance, independently of the solutions; hence all of the extremals for this problem are identified and existence and uniqueness results are obtained.
	epubs.siam.org /sam-bin/dbq/article/19545 (195 words)

	Integration of the Rigid Body Equations of Motion (Site not responding. Last check: 2007-11-06)
		_1 which allows for a system containing a mixture of rigid bodies and atomistic species, provided the rigid bodies are not linked to other species by constraint bonds.
		Thermostats and Barostats It is straightforward to couple the rigid body equations of motion to a thermostat and/or barostat.
		The thermostat is coupled to both the translational and rotational degrees of freedom and so both the translational and rotational velocities are propagated in an analogous manner to the thermostated atomic velocities.
	www.cse.clrc.ac.uk /msi/software/DL_POLY/MANUALS/USRMAN2/node82.html (295 words)

	Rigid Body Dynamics and Dynamical Systems
		A Treatise on the Analytical Dynamics of Particles and Rigid Bodies by E. Whittaker.
		Rigid body kinematics: the description of the motion of systems of rigid bodies.
		Rigid body kinetics: the study of the forces that cause motion and the relationship between the forces and the motion.
	www.seas.upenn.edu /~meam535/fall02 (845 words)

	Torques on a Rigid Body
		If studied independently, the forces acting on a rigid body produce torques (or moments) which tend to cause the body to rotate.
		In this lab the student will be introduced to the concept of torque and examine how torques applied to a rigid body obey Newton’s Law of Equilibrium.
		One common measure of torque is the use of the term "lb-ft" in the automobile industry to describe the rotating force generated by the crankshaft in a car.
	www.gonzaga.org /teachers/mkelley/labs/torque.htm (919 words)

	Rigid body rotation
		It is possible to define an axis of rotation (which, for the sake of simplicity, is assumed to pass through the body)--this axis corresponds to the straight-line which is the locus of all points inside the body which remain stationary as the body rotates.
		A general point located inside the body executes circular motion which is centred on the rotation axis, and orientated in the plane perpendicular to this axis.
		Thus, in a rigidly rotating body, the rotation speed increases linearly with (perpendicular) distance from the axis of rotation.
	farside.ph.utexas.edu /teaching/301/lectures/node99.html (354 words)

	Rigid Body Kinematics Package -- from Mathematica Information Center
		A Mathematica package is presented which provides many commonly used functions in rigid body kinematics.
		Finally, subroutines are provided that compute the matrix relating the attitude parameter rates to the body angular velocity vector, along with the analytic inverse of this matrix.
		With these routines the attitude vector time derivative is computed for a given body angular velocity vector.
	library.wolfram.com /infocenter/MathSource/852 (168 words)

	ADAMS/Flex Release Notes
		After the flexible body has been positioned, the Rigid->Flex dialog box displays a table of markers and connections that are to be migrated from the rigid body to the flexible body.
		That is, the flexible body is treated as a rigid body.
		A flexible body fixed to ground with a fixed joint where a static equilibrium is followed by a dynamic simulation would incorrectly show a displacement in the I marker of the joint when plotting.
	www.mscsoftware.com /support/prod_support/adams/documentation/2005/flex.htm (2344 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		If the supports are arranged is such a way that the reactions are either concurrent or parallel, the reactions are statically indeterminate, and the structure is said to be improperly constrained.
		A two-force body is a rigid body subjected to forces at only two points.
		Even with six or more unknowns, the rigid body will be improperly constrained if the reactions associated with the given supports either are parallel or intersect the same line.
	web.me.unr.edu /jiang/courses/mech241/CHAP04.PPT (294 words)

	Rigid(1) (Site not responding. Last check: 2007-11-06)
		Euler's equation for the motion of a rigid body in a force field are
		What is the corresponding expression for T? (b) Write the differential equations describing the behavior of the rigid body.
		A rigid, symmetrical spaceship is shaped in the form of a cone with a uniform density.
	electron6.phys.utk.edu /phys594/archives/mechanics/Rigid/rigid1.htm (771 words)

	Dynamics of rigid body
		Prior to deriving governing equation of rigid body dynamics, in the next section some basic kinematical relations will be recapitulated.
		is the linear momentum of the rigid body,
		By using a body-fixed coordinate system the components of the inertia tensor of the body with respect to C remain constant.
	www.fsid.cvut.cz /en/U2052/node82.html (458 words)

	Rigid Body Simulation
		My goal for this project was to create a solid framework for simulations of rigid body dynamics, based on the ideas and algorithms of the paper Nonconvex Rigid Bodies with Stacking by Eran Guendelman, Robert Bridson, and Ronald Fedkiw.
		Since my rigid bodies are very basic at the moment, I decided to model all collisions between then implicitly, because the formulas are fairly simple.
		What this project is This project is thus far a simple simulator for rigid body dynamics, although it is a solid framework for future extensions with other types of primitives, nonconvex objects, and more complicated collisions and stacking problems.
	www-cs-students.stanford.edu /~dalewis/cs448a/rigidbody.html (1107 words)

	Timewarp Rigid Body Simulation - Mirtich (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		Abstract: The traditional high-level algorithms for rigid body simulation work well for moderate numbers of bodies but scale poorly to systems of hundreds or more moving, interacting bodies.
		Rigid body dynamics, though a continuous process, exhibits many aspects of a discrete one.
		2: The dynamics of articulated rigid bodies for purposes of animation (context) - William, Mark et al.
	citeseer.ist.psu.edu /mirtich00timewarp.html (475 words)

	Rigid Body Dynamics
		What are Rigid Body Dynamics - A subset of computer simulation that deals with how to represent and implement the animation or dynamic simulation of a rigid collection of points.
		Simulating the motion of a rigid body is based on simulating the motion of a particle.
		Rigid bodies include rotational information, and information representing the change in orientation over time (delta R(t)).
	www.cs.brown.edu /courses/gs007/lect/sim/rigid/slides.html (1083 words)

	MERL – TR2000-017 – Timewarp Rigid Body Simulation
		The traditional high-level algorithms for rigid body simulation work well for moderate numbers of bodies but scale poorly to systems of hundreds or more moving, interacting bodies.
		With modification, the timewarp algorithm can be used in a uniprocessor rigid body simulator to give substantial performance improvements for simulations with large numbers of bodies.
		It addresses issues particular to rigid body simulation, such as collision detection and contact group management, and describes how to incorporate these into the timewarp framework.
	www.merl.com /papers/TR2000-17 (224 words)

	Maya : Dynamics : Rigid Body Simulations
		When creating rigid body objects, it is important to consider the size, mass and various settings.
		Also, remember that passive rigid bodies are not affected by various fields and forces; so they are quite useful for anything that needs to behave like an immovable barrier.
		I can't really tell from this image which rigid bodies are at fault.
	www.digitaltutors.com /digital_tutors/video_details.php?v=101 (355 words)

	[gmx-users] rigid body (Site not responding. Last check: 2007-11-06)
		That will not be as efficient as a program that supports rigid bodies; > but it might be enough.
		Since this is meant to be a simulation under physiological conditions, the computer time lost in computing protein internal degrees of freedom is negligeable.
		Compared to atoms, rigid bodies do have orientation in addition > to position, torques in addition to forces and rotation in addition to > traslation.
	www.gromacs.org /pipermail/gmx-users/2003-May/005415.html (347 words)

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