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Author |
Biess, A.; Flash, T.; Liebermann, D.G. |
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Title  |
Riemannian geometric approach to human arm dynamics, movement optimization, and invariance |
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Year |
2011 |
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Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics |
Abbreviated Journal |
Phys Rev E Stat Nonlin Soft Matter Phys |
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Volume |
83 |
Issue |
3 Pt 1 |
Pages |
031927 |
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Keywords |
Arm/*physiology; Biomechanics; Computer Simulation; Humans; Kinetics; Male; Models, Biological; Models, Statistical; Models, Theoretical; *Movement; Psychomotor Performance/*physiology; Range of Motion, Articular/physiology; Reaction Time/physiology; Space Perception/*physiology; Torque |
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Abstract |
We present a generally covariant formulation of human arm dynamics and optimization principles in Riemannian configuration space. We extend the one-parameter family of mean-squared-derivative (MSD) cost functionals from Euclidean to Riemannian space, and we show that they are mathematically identical to the corresponding dynamic costs when formulated in a Riemannian space equipped with the kinetic energy metric. In particular, we derive the equivalence of the minimum-jerk and minimum-torque change models in this metric space. Solutions of the one-parameter family of MSD variational problems in Riemannian space are given by (reparameterized) geodesic paths, which correspond to movements with least muscular effort. Finally, movement invariants are derived from symmetries of the Riemannian manifold. We argue that the geometrical structure imposed on the arm's configuration space may provide insights into the emerging properties of the movements generated by the motor system. |
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Bernstein Center for Computational Neuroscience, DE-37073 Gottingen, Germany. armin@nld.ds.mpg.de |
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English |
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1539-3755 |
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PMID:21517543 |
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29 |
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Frenkel-Toledo, S.; Levin, M.F.; Berman, S.; Liebermann, D.G.; Baniña, M.C.; Solomon, J.M.; Ofir-Geva, S.; Soroker, N. |
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Title |
Shared and distinct voxel-based lesion-symptom mappings for spasticity and impaired movement in the hemiparetic upper limb |
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Journal Article |
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Year |
2022 |
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Scientific Reports |
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Sci Rep |
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12 |
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1 |
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2045-2322 |
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113 |
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Author |
Carmeli E.; Liebermann, D.G. |
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Title |
The Function of the Aging Hand |
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Book Chapter |
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2007 |
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The Geriatric Rehabilitation Manual |
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Elsevier |
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NY |
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T. L. Kauffman; M. Moran; J. Barr |
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46 |
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Liebermann, D.G.; Franks, I. M. |
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The use of feedback-based technologies in skill acquisition |
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2004 |
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Notational analysis of Sport and Coaching Science |
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E & FN Spon Pub |
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M. Hughes; I.M. Franks |
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45 |
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Author |
Goodman, D.; Liebermann, D.G. |
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Title |
Time-to-contact as a determiner of action: vision and motor control |
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Year |
1992 |
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Vision and Motor Control |
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335-349 |
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Elsevier Pub. Co |
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Amsterdam, Holland |
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D. Elliott; J. Proteau |
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43 |
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