The Discrete Hamel’s Formalism and Energy-Momentum Integrators for the n-dimensional Spherical Pendulum
نویسندگان
چکیده
This paper discusses Hamel’s formalism and its applications to structure-preserving integration of the ndimensional spherical pendulum. It utilizes redundant coordinates in order to eliminate multiple charts on the configuration space of the pendulum as well as nonphysical artificial singularities induced by local coordinates, while keeping the minimal possible degree of redundancy and avoiding integration of differential-algebraic equations. We show that by a suitable choice of reconstruction equation, this approach leads to an energy-momentum integrator for the n-dimensional spherical pendulum. Long-time numerical simulations are performed that compare the numerical performance of the proposed Hamel integrator with Störmer–Verlet and RATTLE.
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