Analytical Dynamics of Discrete Systems

Rosenberg, R. M.; Schmitendorf, W. E.

doi:10.1007/978-1-4684-8318-5

Cited by 300 publications

(144 citation statements)

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“…If this were the only difference in the trajectories of the frog and the ball, then it would remain invisible in the phase portrait where the trajectory simply goes into and comes out of the position axis at velocity equal to 0. This means that a general treatment of trajectory forms might be expected to require something comparable to a state-time space (Rosenberg, 1977) with spatial, temporal, and velocity axes.…”

Section: Notesmentioning

confidence: 99%

Trajectory forms as a source of information about events

Muchisky

Bingham

2002

Perception & Psychophysics

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The ability to use trajectory forms as visual information about events was tested. A trajectory form is defined as the variation in velocity along a path of motion. In Experiment 1, we tested the ability to detect trajectory form differences between simulations of a freely swinging pendulum and a handmoved pendulum. The trajectory form of the freely swinging pendulum was symmetric around the midpoint, whereas the hand moved was not. In Experiment 2, we isolated trajectory form information by varying the amplitudes of events while holding their periods constant. Straight path versions of the harmonic events from Experiment 1 were tested. In Experiment 3, we tested sensitivity to symmetrical peakening or flattening of trajectory forms. Participants detected small differences in all three experiments. In Experiment 4, we tested the ability to identify specific events based only on differences in trajectory forms. Participants were able to identify four different events. We investigated properties of trajectory forms that might potentially be detected and used as information, and we found that the curvature yielded good results.

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Section: Notesmentioning

confidence: 99%

Trajectory forms as a source of information about events

Muchisky

Bingham

2002

Perception & Psychophysics

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“…This theory states that instead of applying constraints which apply forces to a system, the coordinate basis is changed to be orthogonal to the constraint so that the only forces in the system are the real physical forces [25]. However, in terms of modeling and tracking an articulated object, it is only necessary to derive the equations in terms of 3D location and orientation velocities as opposed to the more complicated equations of potential and kinetic energy involved in this theory.…”

Section: Contributionmentioning

confidence: 99%

Kinematic sets for real-time robust articulated object tracking

Comport

Marchand

Chaumette

2007

Image and Vision Computing

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In this article a new approach is given for real-time visual tracking of a class of articulated non-rigid objects in 3D. The main contribution of this paper consists in symmetrically modeling the motion and velocity of an articulated object via a novel kinematic set approach. This is likened to a Lagrange-d'Alembert formulation in classical physics. The advantages of this new model over pre-existing methods include improved precision, robustness and efficiency, leading to real-time performance. Furthermore, a general class of mechanical joints can be considered and the method can track objects where previous approaches have failed due to a lack of visual information. In summary, a joint configuration is modeled by using Pfaffian velocity constraints. The configuration and location of a joint is then used to build a general Jacobian Matrix which relates individual rigid body velocities(twists) to an underlying minimal subspace. A closed loop control law is then derived in order to minimize a set of distance errors in the image and estimate the system parameters. The tracking is locally based upon efficient distance criterion. Experimental results show prismatic, rotational and helical type links and up to eight general parameters. A statistical M-estimation technique is applied to improve robustness. A monocular camera system was used as a real-time sensor to verify the theory.

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“…Here we apply the above methods to the so called constrained particle in Q = IR 3 xyz (see [17], pag. 256, [4], pag.…”

Section: Cartan's Affine Generalized Spaces Developmentmentioning

confidence: 99%