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N-body dynamics on closed surfaces: the axioms of mechanics.

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Title: N-body dynamics on closed surfaces: the axioms of mechanics.
Authors: Boatto, Stefanella1 boatto.stefanella@gmail.com, Dritschel, David G.2, Schaefer, Rodrigo G.3
Source: Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences. Aug2016, Vol. 472 Issue 2192, p1-20. 20p.
Subjects: Particles, Dynamics, Riemann surfaces, Mathematical functions, Kepler's laws, Newton's first law of motion
Abstract: A major challenge for our understanding of the mathematical basis of particle dynamics is the formulation of N-body and N-vortex dynamics on Riemann surfaces. In this paper, we show how the two problems are, in fact, closely related when considering the role played by the intrinsic geometry of the surface. This enables a straightforward deduction of the dynamics of point masses, using recently derived results for point vortices on general closed differentiable surfacesMendowed with a metric g. We find, generally, that Kepler's Laws do not hold. What is more, even Newton's First Law (the law of inertia) fails on closed surfaces with variable curvature (e.g. the ellipsoid). [ABSTRACT FROM AUTHOR]
Copyright of Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences is the property of Royal Society and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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PubType: Academic Journal
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  Data: <searchLink fieldCode="DE" term="%22Particles%22">Particles</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamics%22">Dynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Riemann+surfaces%22">Riemann surfaces</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+functions%22">Mathematical functions</searchLink><br /><searchLink fieldCode="DE" term="%22Kepler's+laws%22">Kepler's laws</searchLink><br /><searchLink fieldCode="DE" term="%22Newton's+first+law+of+motion%22">Newton's first law of motion</searchLink>
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  Data: A major challenge for our understanding of the mathematical basis of particle dynamics is the formulation of N-body and N-vortex dynamics on Riemann surfaces. In this paper, we show how the two problems are, in fact, closely related when considering the role played by the intrinsic geometry of the surface. This enables a straightforward deduction of the dynamics of point masses, using recently derived results for point vortices on general closed differentiable surfacesMendowed with a metric g. We find, generally, that Kepler's Laws do not hold. What is more, even Newton's First Law (the law of inertia) fails on closed surfaces with variable curvature (e.g. the ellipsoid). [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences is the property of Royal Society and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1098/rspa.2016.0020
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        Text: English
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      – SubjectFull: Dynamics
        Type: general
      – SubjectFull: Riemann surfaces
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      – SubjectFull: Mathematical functions
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      – SubjectFull: Kepler's laws
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      – SubjectFull: Newton's first law of motion
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      – TitleFull: N-body dynamics on closed surfaces: the axioms of mechanics.
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              Text: Aug2016
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