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Topic: Rigid body dynamics

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Shannon Stewart

	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.
		In the early 1980's Lodtstedt published the first paper I know of in which the instantaneous dynamic equations of a system of rigid bodies in unilateral contact were formulated as a complementarity problem.
		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)

	1.3.7 Rigid body dynamics with ABAQUS/Explicit (Site not responding. Last check: 2007-10-07)
		A single rigid body is under the action of two springs, with one attached to the rigid body and the other in contact with the rigid body.
		Figure 1.3.7–8 Predicted rigid body translation compared with the analytical solution when mass is distributed at the rigid body surface nodes and two degrees of freedom are active at the reference node.
		Figure 1.3.7–9 Predicted rigid body rotation compared with the analytical solution when mass is distributed at the rigid body surface nodes and two degrees of freedom are active at the reference node.
	atlas.rl.ac.uk /hpc/columbus/abaqus/docs/V6.3_HTMLdocs/books/bmk/ch01s03ach25.html (915 words)

	Rigid Body Constraints (Site not responding. Last check: 2007-10-07)
		The rigid body constraint is used to dynamically control a model shortcut as if it were a rigid object.
		Dynamics, the physics of nature like gravity, is used in several parts of Animation:Master — hair and particles for example.
		The initial position and velocity of the body will be determined by the frames leading up to the time at which the constraint turns on since a right body constraint can be added in the middle of an animation (it will be turned off until that time).
	www.hash.com /htmlHelp/v10.5/CustomHtml/Rigid_Body_Const.htm (331 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)

	EGR 183 Web Pages
		is the acceleration of the mass center of the rigid body, and m is the mass of the body.
		Thus the angular acceleration of the rigid body is strictly in the Z direction.
		Locate the mass center of the rigid body and study its motion as you would study a particle of mass equal to the mass of the rigid body (use sum of the forces is equal to the mass times acceleration).
	www.eng.auburn.edu /department/me/courses/nmadsen/egr183a/e183rb1.html (796 words)

	MEC E 250 - Rigid Body Dynamics (Site not responding. Last check: 2007-10-07)
		To study the motion of a rigid body under the simplifying assumption of planar motion (as opposed to 3-D motion), and to understand why it is of interest to study such a restricted or simplified motion first.
		To study the geometry of motion of a rigid body in a plane without reference to the particular forces causing the motion.
		To study the behaviour of rigid bodies in plane motion by analysing the forces which cause the motion.
	www.mece.ualberta.ca /courses/mec250/LipsettWinter250/250objec.html (403 words)

	Rigid Body Dynamics Algorithm for Parallel Computers
		Although the initial aim was to calculate robot dynamics, the new algorithms were applicable to rigid-body systems in general, and quickly found applications outside the robotics community.
		Starting with a collection of individual rigid bodies (rectangles), the equation of motion of each body is evaluated.
		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)

	EN4: Dynamics and Vibrations (Site not responding. Last check: 2007-10-07)
		An expression for the center of mass of a rigid body is obtained by replacing the summation encountered previously for the center of mass of a collection of particles by an equivalent integral:
		Recall that a rigid body is simply a collection of particles constrained to maintain a constant separation during motions of the body.
		Recall that rigid bodies are systems of particles with particles restricted to move in a way that ensures inter-particle distances remain unchanged.
	www.engin.brown.edu /courses/en4/notes/RigidDynamics/dynmod.htm (3003 words)

	Rigid Body Dynamics and Dynamical Systems
		Rigid body kinetics: the study of the forces that cause motion and the relationship between the forces and the motion.
		Dynamical systems: The study of systems governed by ordinary differential equations including the trajectory of the system, stability, and periodicity.
		A Treatise on the Analytical Dynamics of Particles and Rigid Bodies by E. Whittaker.
	www.seas.upenn.edu /~meam535/fall03/Main.html (918 words)

	Andrew Zaferakis: Rigid Body Dynamics (Site not responding. Last check: 2007-10-07)
		For rigid body and non-volume preserving deformable body simulation, useful information is points along the boundary of the object that are penetrating and the penetration depth for each point.
		An ideal representation of a deformable body is an infinite collection of particles that makeup the boundary of the object.
		A collision force is applied to the rigid body, the green arrow, and also applied to the deformable body, the purple arrows at the two particles.
	www.cs.unc.edu /~andrewz/dynamics/unconstrained.html (1138 words)

	Rigid body dynamics -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-07)
		(additional info and facts about Rigid body) Rigid body (The branch of mechanics concerned with the forces that cause motions of bodies) dynamics differs from particle dynamics in that the body takes up (An area reserved for some particular purpose) space and can rotate, which introduces other considerations.
		However, is the formula for the position of center of mass.
		When learning about angular motion, students are generally first exposed to the case of rotation only in the x-y plane and a fixed axis or axis at the center of mass with constant rotational inertia.
	www.absoluteastronomy.com /encyclopedia/r/ri/rigid_body_dynamics.htm (531 words)

	ipedia.com: Rigid body dynamics Article (Site not responding. Last check: 2007-10-07)
		Rigid body dynamics differs from particle dynamics in that the body takes up space and can rotate, which introduces other consdierations.
		Equations from particle dynamics can be generalized to rigid b...
		The most general equation for rotation of a rigid body in three dimensions about an arbitrary origin O with axes x,y,z is
	www.ipedia.com /rigid_body_dynamics.html (531 words)

	Rigid Body Dynamics
		Simulating the motion of a rigid body is based on simulating the motion of a particle.
		In order to simulate the dynamics of a rigid body at discrete time steps we must use some form of integratiom.
		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)

	Body Dynamics -- Recommendations and Resources (Site not responding. Last check: 2007-10-07)
		Dynamism is the ideal in metaphysical cosmology which explains the material world in terms of active, pointlike ''forces,'' with no extension but with action at a distance.
		Dynamism is a term coined by libertarian pundit Virginia Postrel to describe her social philosophy that embraces cultural change, individual choice, and the open society.
		She contrasts dynamism with what she calls "stasis" — that is, government regulation and conservative resistance to change.
	www.becomingapediatrician.com /health/19/body-dynamics.html (1019 words)

	Trinkle's Rigid Body Dynamics (Site not responding. Last check: 2007-10-07)
		Roughly speaking, in rigid body dynamics, the w and z vectors represent relative accelerations and contact forces expressed in coordinate frames attached to the contact points (assumed isolated).
		Methods for simulating dynamic rigid body systems are still not mature; only now are algorithms becoming available in commercial software.
		Here are some papers related to rigid body dynamics simulation: theory, velocity-base time-stepping, theory and examples with torsional friction, the quasistatic problem.
	www.cs.sandia.gov /~jctrink/rigid_body_dynamics.html (609 words)

	Rigid Body Dynamics and Dynamical Systems
		MEAM 535 is a graduate level course in rigid body dynamics and dynamical systems.
		The course will emphasize the tools of analytical mechanics with the main goal of developing mathematical models that describe the dynamics of systems of rigid bodies and continuous systems.
		The main focus will be on analytical mechanics, a set of principles that allow us to write the equations of motion using analytical methods (as opposed to graphical or numerical methods).
	www.seas.upenn.edu /~meam535/fall02 (845 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)

	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 (320 words)

	ES223: Rigid Body Dynamics -- Fall 2004 (Site not responding. Last check: 2007-10-07)
		Teach students the fundamental principles of kinematics and dynamics of particles, systems of particles, and rigid bodies (Newtonian mechanics).
		Students will be capable of modeling the dynamics of a system composed of rigid bodies by applying the first principles of Newtonian mechanics.
		Students will be able to demonstrate their competence in interpreting their mathematical solution to a dynamical rigid body problem.
	people.clarkson.edu /~taylorja/es223/fall2004/resources/syllabus.html (521 words)

	Trinkle's Survey of Multibody Dynamics Software
		It also uses a "fixed set of bodies instead of triangular meshes." Complementarity theory and Baraff's method are mentioned as worthy goals that are not implemented.
		A rigid body dynamics engine developed by Arachi.com that is based on the algorithms of Featherstone (dynamics with bilateral constraints), Mirtich (collision impulse response), and Baraff (contact transitions e.g., sticking to sliding).
		The integration method for rigid body dynamics is a penalty method.
	www.cs.rpi.edu /~trink/sim_packages.html (1187 words)

	Rigid Body Dynamics
		Note that as this problem involves only a single moving rigid body, it is implicit that the angular velocity vector refers to that body.
		The kinetic energy of a rigid body rotating about a fixed axis through a fixed point in space is equal to 1/2 the mass moment of inertia of the body about that axis multiplied by the square of the body angular velocity.
		The internal energy of a rigid body at constant temperature is unchanging.
	www.eng.auburn.edu /department/me/courses/nmadsen/mech2120/p1a.html (5890 words)

	Rigid Body Dynamics (Site not responding. Last check: 2007-10-07)
		Dynamics of a rigid body with fixed point under different force fields
		Dynamics of a rigid body suspended by a string
		Dynamics of a rigid body on a surface considering different types of interaction between them
	mech.math.msu.su /English/department/teormech/area4.htm (111 words)

	Dynamics of Rigid Bodies (Site not responding. Last check: 2007-10-07)
		Kinematics and dynamics of particles and rigid bodies in one, two, and three dimensions.
		Objective 1: To teach students the basic principles underlying the dynamics of rigid bodies in planar and 3D motion (B).
		3.2 Students will be able to evaluate the kinetic energy of rigid bodies as well as the potential energy associated with gravity and spring forces (1,2,3).
	www.me.gatech.edu /me/semester_conversion/ME2202.html (426 words)

	Rigid Body Dynamics
		A rigid body is a body in which the distances between all its component particles remain fixed under the application of a force or torque.
		A rigid body therefore conserves its shape during its motion.
		In the dynamics of the rigid body the toral angles have very intuitive meanings of rotation, precession and nutation.
	www.iram.rwth-aachen.de /~Heinz/rigid.html (610 words)

	Chris Hecker's Rigid Body Dynamics Information
		Milestone: You should have a 3D rigid body simulator at this point, with an appropriate orientation representation chosen by understanding and weighing the advantages and disadvantages of the different methods.
		Up to this point, we have some amazing simulations going, but our object are all individual rigid bodies, without joints between them to hold them together (although the adventurous among you might have tried to use springs to build an articulated rigid body, with varying levels of success).
		Milestone: You should be able to link two or more rigid bodies with different kinds of joints, and derive the constraint equations and the constraint Jacobian matrix.
	www.d6.com /users/checker/dynamics.htm (4229 words)

	Courses \| Conference: SIGGRAPH 2005
		A comprehensive overview of articulated-rigid-body dynamics simulation based on Featherstone's recursive method and supplemented with analytical constraints, impact, frictional contact, joint-space control, and implicit integration.
		Familiarity with physically based simulation techniques, rigid-body dynamics, collision detection, kinematics of articulated bodies, numerical linear algebra, differential equations, and numerical methods.
		This course is intended for practitioners with some experience in physically based modeling and an interest in articulated body simulation.
	www.siggraph.org /s2005/main.php?f=conference&p=courses&s=2 (209 words)

	Rigid Body Dynamics, Second Course (Site not responding. Last check: 2007-10-07)
		To develop the knowledge of rigid body dynamics to a level where the motion as a function of time of a rigid body in three dimensions can be analyzed and solved, with the aid of a computer.
		The examination is in the form of computer assignments, using Matlab and a commercial code for rigid body dynamics.
		Coordinate transformations, Coriolis equation, moment of momentum, the inertia tensor, inertial systems, the equations of motion, the Euler angles, the Euler parameters, applications such as gyroscopic instruments.
	www.mekanik.ikp.liu.se /ueduc/tmme19/mekfk.html (129 words)

	Rigid Body Dynamics (Site not responding. Last check: 2007-10-07)
		This is a webpage for my cand.scient degree in computer science at the university of Oslo, faculty of natural science, institute of computer science, direction of mathematical modeling and group of simulation and visualization.
		The goal of my thesis is to look at simulation of rigid body dynamics and write a library that can easily be reused by people without much physics knowledge.
		This page is a work in progress, most of the info here is also included in the sources.
	folk.uio.no /staalep/hfag/index.shtml (114 words)

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