Criteria of chaos in non-linear mechanics |
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| Affiliation: | 1. Department of Civil Engineering, School of Engineering, University of Birmingham, Birmingham B15 2TT, United Kingdom;2. Birmingham Centre for Railway Research and Education, School of Engineering, University of Birmingham, Birmingham B15 2TT, United Kingdom |
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| Abstract: | The transition to chaos in non-linear mechanics can be characterized by the divergency of trajectories in configuration space with the kinematic line-element. Geometrical interpretation of this transition allows us to express the criteria of chaos in terms of the curvature of the configuration space and the geodesic curvature of the trajectories. In this work analytical criteria of chaos based upon the concept of orbital instability in the configuration space are derived. |
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