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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   (2985 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)

Orientation (rigid body)   (Site not responding. Last check: 2007-10-26) Orientation may be visualized by attaching a basis of tangent vectors to an object. If the rigid body has any rotational symmetry, not all orientations are distinguishable, except by observing how the orientation evolves in time from a known starting orientation. This meaning of orientation should not be confused with the other meaning, where a different orientation means a change to the mirror image by an improper rotation, which includes a reflection, see orientation (mathematics). www.guideofpills.com /Orientation_%28rigid_body%29.html   (379 words)

orientation - Search Results - MSN Encarta Market Orientation, production of goods that are carefully researched and designed to appeal to customers in the market. *orientation (mental) *sexual orientation *Orientation (rigid body) *Orientation week, the first week of a university year in New Zealand and Australia *in... Sexual orientation describes the direction of an individual's sexuality, often in relation to their own sex or gender. encarta.msn.com /encnet/refpages/search.aspx?q=orientation   (155 words)

Kinematics A rigid body may be positioned by locating the position of one point of the body (3 co-ordinates), then positioning a line on the body (2 co-ordinates) and finally identifying a rotation about the line (1 co-odinates). If the same rigid body is rotated from a position "A" through and an angle of π/2 about the y axis and then is rotated π/2 about the x axis it has been moved to a position "C" which is not the same as "B". For a body possessing linear plus angular motion it is often not possible to have an instantaneous axis of rotation because all points may have non-zero velocities. www.roymech.co.uk /Useful_Tables/Mechanics/kinematics.html   (0 words)

Orientation (rigid body) - Wikipedia, the free encyclopedia Orientation may be visualized by attaching a basis of tangent vectors to an object. If the rigid body has any rotational symmetry, not all orientations are distinguishable, except by observing how the orientation evolves in time from a known starting orientation. This meaning of orientation should not be confused with the other meaning, where a different orientation means a change to the mirror image by an improper rotation, which includes a reflection, see orientation (mathematics). en.wikipedia.org /wiki/Orientation_(rigid_body)   (299 words)

Body (SimMechanics) The mass is the body's inertia and controls the translational acceleration of the CG in response to an applied force. The orientation of the CG CS axes with respect to another CS external to the body (the World CS, a CS on a Ground, or a CS on another Body) then determines the orientation of the body with respect to other bodies or with respect to World. The initial orientation is set by its inertia tensor components (in the CG CS) and the orientation of the CG CS axes with respect to other CSs in the machine. mathworks.com /access/helpdesk_r13/help/toolbox/physmod/mech/body.html   (1967 words)

Rigid body - Wikipedia, the free encyclopedia In physics, a rigid body is an idealization of a solid body of finite size in which deformation is neglected. In classical mechanics a rigid body is usually considered as a continuous mass distribution, while in quantum mechanics a rigid body is usually thought of as a collection of point masses. The configuration space of a rigid body with one point fixed (i.e., a body with zero translational motion) is given by the underlying manifold of the rotation group SO(3). en.wikipedia.org /wiki/Rigid_body   (947 words)

Classical Mechanics   (Site not responding. Last check: 2007-10-26) A rigid body is a system of particles in which the distances between the particles do not vary. Thus a rigid body is a mechanical system with six degrees of freedom. The equations of motion of a rigid body are move-it.com.ru   (426 words)

Deformation Defined With rigid body deformation the position and orientation of points in a rock body relative to an internal reference frame are not changed. Non-rigid body deformation is different than rigid body deformation in that the position and orientation of points within a rock body are changed relative to both an internal and external reference frame. Distortion is a non-rigid body operation that involves the change in the spacing of points within a body of rock in such a way that the overall shape of the body is altered with or without a change in volume (Figure 26). www.geology.sdsu.edu /visualstructure/vss/htm_hlp/def_d.htm   (0 words)

Rigid Body Collision Response We demonstrate that considering the motion of the rigid bodies is necessary for correct collision response. Position of a rigid body in space is characterized by a translation vector and a rotation. The rigid body's linear momentum can be changed by an application of force F acting in the center of mass. www.cescg.org /CESCG-2003/LKavan   (4814 words)

The Role of Rotation in Rigid and Deformable Body Mechanics Kinematics of a rigid body concern the effects of motion, as opposed to causes. A rigid body considered to be isolated from all others has six motional degrees of freedom, three of which describe translation of the center of mass, and the remaining three describe rotation about a point fixed at the center of mass. Orientation of a body of arbitrary shape can be defined in terms of three mutually orthogonal axes embedded in the body. webpages.charter.net /glennbowie/rotate.html   (0 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)

eMedicine - Foreign Body Aspiration : Article by Martin E Warshawsky, MD, FACP, FCCP The presence of a foreign body and its condition, anatomic location (eg, larynx; trachea; main, lobar, or segmental bronchus), shape, composition, position, and extent of entrapment by edema or granulation tissue must be identified prior to extraction attempts. Rigid bronchoscopy is the procedure of choice for removing foreign bodies in children and in most adults. As with rigid bronchoscopy, it is imperative to practice grasping an identical object outside of the body before attempting to manipulate the aspirated object. www.emedicine.com /med/topic810.htm   (0 words)

Rigidly Re-Orienting An Extended Body It follows that, as Rindler says, "the motion of one point of a rigidly moving body determines that of all the others", because the rotational degrees of freedom of a rigidly moving object are restricted by the fact that its state of rotation cannot be changed. Since it's impossible to change the rotational state of a rigid body, and since this particular disk (by assumption) is not rotating, it might be tempting to think that its spatial orientation can never change. This is because the Thomas precession experienced by a segment depends on the orientation of that segment relative to the translational velocity vector. www.mathpages.com /home/kmath495/kmath495.htm   (0 words)

ode.Body   (Site not responding. Last check: 2007-10-26) The rigid body class encapsulating the ODE body. This class represents a rigid body that has a location and orientation in space and that stores the mass properties of an object. Note that a disabled body that is connected through a joint to an enabled body will be automatically re-enabled at the next simulation step. pyode.sourceforge.net /api/public/ode.Body-class.html   (949 words)

Moment of Inertia Newton's first law of motion says "A body maintains the current state of motion unless acted upon by an external force." The measure of the inertia in the linear motion is the mass of the system and its angular counterpart is the so-called moment of inertia. A rigid body can be considered as a system of particles in which the relative positions of the particles do not change. Thus, it would be more accurate to say that the moment of inertia of a rigid body reflects the mass distribution within the body with respect to the axis of rotation. kwon3d.com /theory/moi/moi.html   (0 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   (0 words)

Observing a Translating, Rotating Rigid Body :: Understanding Mechanical Concepts (SimMechanics) You can obtain the special case essential for rigid body motion by letting O be the CG CS of an extended rigid body (the origin of O at the CG itself) and letting b be a point somewhere in the same body. You state a body's orientation by specifying the tilt of its center of gravity coordinate system (CG CS) axes relative to some other set of axes, either the CG CS axes of another body or the World CS axes. One Euler angle convention is to rotate about one body coordinate axis (which rotates the other two); then rotate about a second body coordinate axis (rotated from its original direction); and lastly, rotate about the first body coordinate axis again (which axis has been rotated into a new direction by the second rotation). www.mathworks.com /access/helpdesk_r13/help/toolbox/physmod/mech/mech_review3.html   (0 words)

The Kinematic Geometry of Rigid Body Displacements. Any rigid objects position in 2-D space is determined by the positions of at least two distinct points of that object. Any rigid objects position in 3-D space is determined by the positions of at least three distinct non-collinear points of that object. Since analysis is reduced from examining three points of a body to two, let's choose points A and B as the two examined in the planar displacements of triangle ABO. members.aol.com /mszlazak/kinematics.html   (2409 words)

[No title]   (Site not responding. Last check: 2007-10-26) In this work we present (1) a method for determining the orientation of the axis of symmetry of a cylindrical marker in a tomographic image and (2) an extension to the standard approach to rigid-body registration that utilizes the orientation of marker axes as an adjunct to the positions of their centroids. Accurate measurement of the orientation of that axis is made difficult by the typically small size of the marker relative to the voxel sizes and by noise present in the typical MR or CT image. The orientations of the marker axes provide information about the relative rotation of the two spaces about all axes except themselves, and that information is more accurate for axes that are more perpendicular to the marker axes. www.vuse.vanderbilt.edu /~jmf/vita_in_Word/papers/Liu_2003_Medim_orientation.doc   (4367 words)

Open Dynamics Engine Note that the shape of a rigid body is not a dynamical property (except insofar as it influences the various mass properties). Axis 1 is attached to body 1, and axis 2 is attached to body 2. The angle is measured between a body and the cross, or between the static environment and the cross. ode.org /ode-latest-userguide.html   (14904 words)

Rigid body motion To describe the motion of a rigid body we use two systems of coordinates, a space-fixed system X, Y, Z, and a moving system x, y, z, which is rigidly fixed in the body and participates in its motion. The orientation of the axes of that system relative to the axes of the space-fixed system is given by three independent angles. The orientation of the body-fixed coordinate system with respect to the space-fixed coordinate system is described by three angles. electron6.phys.utk.edu /phys594/Tools/mechanics/summary/rigid/rigid.htm   (372 words)

Dead Reckoning for Walking Robots To solve this, a coordinate system called the body frame is assigned to the robot; another coordinate system, called the world frame, is assigned to a fixed frame of reference. The problem, then, is to find the rigid body transformation (matrix R and vector T)-that is, to determine the position and orientation of the robot in the world based on the positions of the feet- that maps foot positions (Pb) in the body frame into foot positions (Pw) in the world frame. Solve for the rigid body transformation that best transforms foot positions in body coordinates to the world coordinate system, using a technique based on singular value decomposition. ranier.hq.nasa.gov /telerobotics_page/Technologies/0403.html   (654 words)

Free Rigid Body Consider a free rigid body subject to a dead load. The last entity is called a body; it adds an inertial contribution to the dynamic degrees of freedom of the node. It also has ``null'' arm with respect to the node, and the amplitude is constant and equal to the gravity acceleration (the ``const, '' is optional, as a number is interpreted as a constant by default). www.aero.polimi.it /~mbdyn/documentation/tutorials/node6.html   (0 words)

Orientation - WikEd The orientation should cover all technology likely to be encountered in the course, providing tutorials or instructions and giving an assignment to complete to show mastery (or at least familiarity). These orientations usually include training in the campus computing systems and passwords as well as an introdcution to the course management system at that college. Individual instructors should ALSO post orientation activities in the individual courses, but these should be dovetailed with what the college offers, so that students do not repeat activities. wik.ed.uiuc.edu /index.php?title=Orientation&printable=yes   (323 words)

Articulated Body Tracking The human body models can be simple as the articulated body skeleton with connected segments [Cham99] [Song00] or 2-D patches-based models [Ju96] [Bregler98][Jojic99], and even be complex as volumetric models with combinations of elementary volumes [Deutscher00] [Sidenbladh00] [Yamamoto00]. We define each body part as an isosceles trapezoidal planar patch either from the front view 1(a) or from the side view 1(b), and those patches are linked together by the kinematic chains in a hierarchical manner shown in 1(c). One possibility is to use a “divide-and-conquer technique” where an articulated object is decomposed into a number of primitive (rigid or articulated) sub-parts; one solves for motion and depth of the sub-parts and verifies whether the parts satisfy the necessary constraints. www.ifp.uiuc.edu /~yuhuang/Body.html   (0 words)

semirigid.html   (Site not responding. Last check: 2007-10-26) The principal geometrical axes of the ellipsoid (shown by white segments in all the animations) lie along the principal axes of inertia of the body, with the longest geometrical axis along the minor principal axis of inertia and the shortest along the major principal axis of inertia. The white segments in the animations thus show the instantaneous orientation of the principal axes frame of the body. The animation on the right shows the rotational motion that results when the initial angular velocity of the body is close to its minor principal axis of inertia, which is also the longest geometrical axis of the ellipsoid. www.aero.iitb.ac.in /~bhat/semirigid.html   (380 words)

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