Bibliographic Details
| 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] |
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| Database: |
Engineering Source |
