相关论文: Rolling balls and Octonions

A simple derivation of the classical solutions of a nonlinear model describing a harmonic oscillator on the sphere and the hyperbolic plane is presented in polar coordinates. These solutions are then related to those in cartesian…

We study curvature invariants of a sub-Riemannian manifold (i.e., a manifold with a Riemannian metric on a non-holonomic distribution) related to mutual curvature of several pairwise orthogonal subspaces of the distribution, and prove…

We derive a collisionless kinetic theory for an ensemble of molecules undergoing nonholonomic rolling dynamics. We demonstrate that the existence of nonholonomic constraints leads to problems in generalizing the standard methods of…

After early work of Henon it has become folk knowledge that symmetric periodic orbits are of particular importance. We reinforce this belief by additional studies and we further find that invariant closed symplectic submanifolds caused by…

Balancing square and rectangular tables by rotation has been a interesting way to illustrate the intermediate value theorem. The aim of this note is to show that the balancing act but with non-rectangular tables can be a nice application of…

A generalization of the concept of PT-symmetric Hamiltonians H=p^2+V(x) is described. It uses analytic potentials V(x) (with singularities) and a generalized concept of PT-symmetric asymptotic boundary conditions. Nontrivial toboggans are…

We give an informal summary of ongoing work which uses tools distilled from the theory of fibre bundles to classify and connect invariant fields associated with spin motion in storage rings. We mention four major theorems. One ties…

In this paper, we use methods from differential geometry and statistical mechanics to investigate a model for the concept of mass. The theory is not quantum mechanical in the usual sense, although certain features like multiple histories…

We develop a complete mathematical theory for the symmetrical solutions of the generalized nonlinear Schr\"odinger equation based on the new concept of angular pseudomomentum. We consider the symmetric solitons of a generalized nonlinear…

A widely used mathematical model for the bouncing motion of an ideally elastic ball -- referred to in previous work by the first two authors and collaborators as a {\em no-slip billiard} system -- exhibits some notable dynamical behavior…

We develop a quasisymmetric analogue of the theory of Schubert cycles, building off of our previous work on a quasisymmetric analogue of Schubert polynomials and divided differences. Our constructions result in a natural geometric…

General topologically invariant microscopical expressions for quantum numbers of particle-like solitons ("skyrmions") are derived for a class of (2+1)D models. Skyrmions are either half-integer spin fermions with odd electric charge or…

We investigate both the quantum and classical dynamics of a non-Hermitian system via a kicked rotor model with $\mathcal{PT}$ symmetry. For the quantum dynamics, both the mean momentum and mean square of momentum exhibits the staircase…

This is a short survey paper, partly meant as a research announcement. Its purpose is to highlight some aspects of the interplay between quantales, inverse semigroups, and groupoids. Many of the results mentioned have not yet been presented…

In a previous work, both the constants of motion of a classical system and the symmetries of the corresponding quantum version have been computed with the help of factorizations. As their expressions were not polynomial, in this paper the…

This paper focuses on rotational phenomena of rigid body kinematics. It discusses them in a group-theoretic approach as completely as possible, using methods and notations as intuitive as possible. With a review of current literature, this…

This paper introduces a new approach to finding knots and links with hidden symmetries using "hidden extensions", a class of hidden symmetries defined here. We exhibit a family of tangle complements in the ball whose boundaries have…

We determine approximate numerical integrals of motion of 2D symmetric Hamiltonian systems. We detail for a few gravitational potentials the conditions under which quasi-integrals are obtained as polynomial series. We show that each of…

This paper is devoted to several new results concerning (standard) octonion polynomials. The first is the determination of the roots of all right scalar multiples of octonion polynomials. The roots of left multiples are also discussed,…

We establish new explicit connections between classical (scalar) and matrix Gegenbauer polynomials, which result in new symmetries of the latter and further give access to several properties that have been out of reach before: generating…