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When one considers a rigid body undergoing a plane motion, which is essentially a blend of translational and rotational movement, the application of Newton's second law gives the formula for the translational movement of such a body. If this equation is multiplied by a time interval, dt, and then integrated over the limits of integration, it results in an equation that embodies the principle of linear impulse.
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Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion
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Minimum action principle and shape dynamics.

Patrice Koehl1

  • 1Department of Computer Science and Genome Center, University of California, Davis, CA 95616, USA koehl@cs.ucdavis.edu.

Journal of the Royal Society, Interface
|May 19, 2017
PubMed
Summary
This summary is machine-generated.

This study introduces a novel shape distance metric based on deformation cost, outperforming experts in primate bone and tooth analysis for shape recognition and evolutionary pattern identification.

Keywords:
biological shapesconformal mapsminimum action path

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Area of Science:

  • Computational geometry
  • Geometric morphometrics
  • Mathematical modeling

Background:

  • Comparing 3D shapes often relies on direct geometric property analysis.
  • Existing methods may not fully capture intrinsic shape relationships.
  • Understanding shape variation is crucial in fields like evolutionary biology.

Purpose of the Study:

  • To develop a new method for computing distances between 3D shapes.
  • To introduce a shape distance metric based on deformation cost.
  • To apply this metric to analyze primate skeletal and dental morphology.

Main Methods:

  • Computed shape distance via the cost of deforming one shape into another.
  • Utilized the geodesic path in the space of shapes, minimizing Onsager-Machlup action.
  • Defined an elastic energy for shapes to establish an intrinsic quasi-metric.

Main Results:

  • The proposed variational quasi-metric effectively measures shape differences.
  • Demonstrated strong performance in shape recognition tasks.
  • Successfully identified evolutionary patterns in primate bone and tooth datasets.
  • Achieved success rates comparable to or exceeding expert observers.

Conclusions:

  • The novel deformation-based shape distance metric is a powerful tool.
  • This method offers a robust approach for quantitative shape analysis.
  • The technique shows significant potential in geometric morphometrics and evolutionary studies.