Point mass dynamics on spherical hypersurfaces
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The equations of motion are derived for a system of point masses on the (hyper-)surface Sn of a sphere embedded in ℝn+1 for any dimension n > 1. Due to the symmetry of the surface, the equations take a particularly simple form when using the Cartesian coordinates of ℝn+1. The constraint that the distance of the jth mass‖rj‖ from the origin remains constant (i.e. each mass remains on the surface) is automatically satisfied by the equations of motion. Moreover, the equations are a Hamiltonian system with a conserved energy as well as a host of conserved angular momenta. Several examples are illustrated in dimensions n = 2 (the sphere) and n= 3 (the glome).
Dritschel , D G 2019 , ' Point mass dynamics on spherical hypersurfaces ' , Philosophical Transactions of the Royal Society. A, Mathematical, Physical and Engineering Sciences , vol. 377 , no. 2158 , 20180349 , pp. 1-11 . https://doi.org/10.1098/rsta.2018.0349
Philosophical Transactions of the Royal Society. A, Mathematical, Physical and Engineering Sciences
© The Authors 2019. This work has been made available online in accordance with the publisher's policies. This is the author created accepted version manuscript following peer review and as such may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1098/rsta.2018.0349
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