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A general recipe is developed for the study of rigid body dynamics in terms of Poincare surfaces of section. A section condition is chosen which captures every trajectory on a given energy surface. The possible topological types of the corresponding surfaces of section are determined, and their 1:1 projection to a conveniently defined torus is proposed for graphical rendering.
Over any smooth algebraic variety over a $p$-adic local field $k$, we construct the de Rham comparison isomorphisms for the etale cohomology with partial compact support of de Rham $mathbb Z_p$-local systems, and show that they are compatible with Po
Quantum manifestations of the dynamics around resonant tori in perturbed Hamiltonian systems, dictated by the Poincare--Birkhoff theorem, are shown to exist. They are embedded in the interactions involving states which differ in a number of quanta eq
Mission designers must study many dynamical models to plan a low-cost spacecraft trajectory that satisfies mission constraints. They routinely use Poincare maps to search for a suitable path through the interconnected web of periodic orbits and invar
Accurately modeling contact behaviors for real-world, near-rigid materials remains a grand challenge for existing rigid-body physics simulators. This paper introduces a data-augmented contact model that incorporates analytical solutions with observed
We present Brax, an open source library for rigid body simulation with a focus on performance and parallelism on accelerators, written in JAX. We present results on a suite of tasks inspired by the existing reinforcement learning literature, but rema