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In real-world robotics applications, accurate models of robot dynamics are critical for safe and stable control in rapidly changing operational conditions. This motivates the use of machine learning techniques to approximate robot dynamics…

Robotics · Computer Science 2022-01-13 Thai Duong , Nikolay Atanasov

This paper presents the classification, over the fields of real and complex numbers, of the minimal ${\mathbb Z}_2\times{\mathbb Z}_2$-graded Lie algebras and Lie superalgebras spanned by $4$ generators and with no empty graded sector. The…

Mathematical Physics · Physics 2021-06-21 Zhanna Kuznetsova , Francesco Toppan

We define a coupling of two baker maps through a pi/2 rotation both in position and in momentum. The classical trajectories thus exhibit spiraling, or loxodromic motion, which is only possible for conservative maps of at least two degrees…

Chaotic Dynamics · Physics 2015-06-26 Pedro R. del Santoro , Raul O. Vallejos , Alfredo M. Ozorio de Almeida

The automorphisms of a two-generator free group acting on the space of orientation-preserving isometric actions of on hyperbolic 3-space defines a dynamical system. Those actions which preserve a hyperbolic plane but not an orientation on…

Dynamical Systems · Mathematics 2016-10-11 William Goldman , Greg McShane , George Stantchev , Ser Peow Tan

This paper presents a generalization of conventional sliding mode control designs for systems in Euclidean spaces to fully actuated simple mechanical systems whose configuration space is a Lie group for the trajectory-tracking problem. A…

Optimization and Control · Mathematics 2023-06-01 Eduardo Espindola , Yu Tang

We describe a new and robust method to prove rigidity results in complex dynamics. The new ingredient is the geometry of the critical puzzle pieces: under control of geometry and ``complex bounds'', two generalized polynomial-like maps…

Dynamical Systems · Mathematics 2018-01-08 Daniel Smania

Maximal parabolic subalgebras of untwisted affine Kac-Moody algebras were studied in the context of Borel-de Siebenthal theory in [13], where they were realized as certain equivariant map algebras with a non-free abelian group action. In…

Quantum Algebra · Mathematics 2025-05-21 Kudret Bostanci , Deniz Kus

We consider the existence of invariant curves of real analytic reversible mappings which are quasi-periodic in the angle variables. By the normal form theorem, we prove that under some assumptions, the original mapping is changed into its…

Dynamical Systems · Mathematics 2023-05-16 Yan Zhuang , Daxiong Piao , Yanmin Niu

Quantum mechanical systems with position dependent masses (PDM) admitting for and more dimensional symmetry algebras are classified. Namely, all PDM systems are specified which, in addition to their invariance w.r.t. a three parametric Lie…

Mathematical Physics · Physics 2023-02-28 A. G. Nikitin

We study a three dimensional non-commutative space emerging in the context of three dimensional Euclidean quantum gravity. Our starting point is the assumption that the isometry group is deformed to the Drinfeld double D(SU(2)). We…

High Energy Physics - Theory · Physics 2009-06-12 E. Joung , J. Mourad , K. Noui

Although inverse kinematics of serial manipulators is a well studied problem, challenges still exist in finding smooth feasible solutions that are also collision aware. Furthermore, with collaborative service robots gaining traction,…

Robotics · Computer Science 2023-11-01 Salih Marangoz , Rohit Menon , Nils Dengler , Maren Bennewitz

By combining the ideas of Cartan's equivalence method and the method of the equivariant moving frame for pseudo-groups, we develop an efficient method for solving equivalence problems arising from horizontal Lie pseudo-group actions. The…

Differential Geometry · Mathematics 2018-11-02 Orn Arnaldsson

We introduce a generalization of the Euclidean algorithm for rings equipped with an involution, and completely enumerate all isomorphism classes of orders over definite, rational quaternion algebras equipped with an orthogonal involution…

Number Theory · Mathematics 2020-06-15 Arseniy , Sheydvasser

In the present work, we demonstrate how the pseudoinverse concept from linear algebra can be used to represent and analyze the boundary conditions of linear systems of partial differential equations. This approach has theoretical and…

Numerical Analysis · Mathematics 2024-01-05 Pelle Olsson

text of abstract (We present a utilitarian review of the family of matrix groups $Sp(2n,\Re)$, in a form suited to various applications both in optics and quantum mechanics. We contrast these groups and their geometry with the much more…

Quantum Physics · Physics 2009-10-28 Arvind , B. Dutta , N. Mukunda , R. Simon

A sequence of large invertible matrices given by a small random perturbation around a fixed diagonal and positive matrix induces a random dynamics on a high-dimensional sphere. For a certain class of rotationally invariant random…

Mathematical Physics · Physics 2019-07-29 Florian Dorsch , Hermann Schulz-Baldes

We consider the quantum inverse scattering method for several mixed integrable models based on the rational SU(N) R-matrix with general toroidal boundary conditions. This includes systems whose Hilbert spaces are invariant by the discrete…

Exactly Solvable and Integrable Systems · Physics 2009-11-10 G. A. P. Ribeiro , M. J. Martins

The so-called equation of motion method is useful to obtain the explicit form of the eigenvectors and eigenvalues of certain non self-adjoint bosonic Hamiltonians with real eigenvalues. These operators can be diagonalized when they are…

Quantum Physics · Physics 2015-09-03 Natalia Bebiano , Joao da Providencia , Joao P. da Providencia

A method for deriving superintegrable Hamiltonians with a spin orbital interaction is presented. The method is applied to obtain a new superintegrable system in Euclidean space $\mathbb{E}_3$ with the following properties. It describes a…

Mathematical Physics · Physics 2015-06-18 D. Riglioni , O. Gingras , P. Winternitz

In this paper we consider families of holomorphic maps defined on subsets of the complex plane, and show that the technique developed in \cite{LSvS1} to treat unfolding of critical relations can also be used to deal with cases where the…

Dynamical Systems · Mathematics 2023-02-08 Genadi Levin , Weixiao Shen , Sebastian van Strien