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N body dynamics on closed surfaces : the axioms of mechanics

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Figure

Figure 1. Such surfaces permit a straightforward, explicit formulation [13].
Figure 2. Dynamics of a single particle, initially at rest, on an oblate ellipsoid of revolution
Figure 3. Consider the unit sphere S2 and a mass m1 fixed at the north pole. The force on a second mass m2 at aco-latitude θ is proportional to 1/ sin2 θ if derived from the potential U(θ) = −γ m˜1m2 cot θ, whereas it is proportionalto sin θ/(1 − cos θ) if derived from the potential U(θ) =γ4π m1m2 ln(1 − cos θ).

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