Related papers: A New Approach in Plane Kinematics
The space-time of modern physics is tailored on light. We rigorously construct the basic entities needed by kinematics: geometry of the physical space and time, using as tool electromagnetic waves, and particularly light-rays. After such a…
A class of analytic planar 3-RPR manipulators is analyzed in this paper. These manipulators have congruent base and moving platforms and the moving platform is rotated of 180 deg about an axis in the plane. The forward kinematics is reduced…
In this work we develop a well-defined theory of orbit spaces for piecewise smooth vector fields (PSVFs). This approach is inspired by the techniques already used in the study of endomorphisms, namely inverse limit analysis, and has been…
The area of research called \textquotedblleft Lineability\textquotedblright% \ looks for linear structures inside exotic subsets of vector spaces. In the last decade lineability/spaceability has been investigated in rather general settings;…
A simple geometrical model is presented for the gravity-driven motion of a single particle on a rough inclined surface. Adopting a simple restitution law for the collisions between the particle and the surface, we arrive at a model in which…
In this Thesis we develop the geometric formulations for higher-order autonomous and non-autonomous dynamical systems, and second-order field theories. In all cases, the physical information of the system is given in terms of a Lagrangian…
This paper provides an overview of selected results and open problems in the theory of hyperplane arrangements, with an emphasis on computations and examples. We give an introduction to many of the essential tools used in the area, such as…
We discuss kinematical properties of a free relativistic particle with deformed phase space in which momentum space is given by (a submanifold of) de Sitter space. We provide a detailed derivation of the action, Hamiltonian structure and…
In this paper a special group of bijective maps of a normed plane, called the group of general rotations, is introduced; it contains the isometry group as a subgroup. The concept of general rotations leads to the notion of flexible motions…
This is a survey article on the theory of lattice points in large planar domains and bodies of dimensions 3 and higher, with an emphasis on recent developments and new methods, including a lot of results established only during the last few…
A new approach to relativistic mechanics is proposed, suitable to describe dynamics of different kinds of relativistic particles. Mathematically it is based on an application of the recent geometric theory of nonholonomic systems on fibred…
We give a critical analysis of the conceptual foundations of special relativity. We formulate a simple operational criterion for distinguishing between noninertial and inertial frames which is introduced prior to geometry. We associate the…
Dense suspensions of particles are relevant to many applications and are a key platform for developing a fundamental physics of out-of-equilibrium systems. They present challenging flow properties, apparently turning from liquid to solid…
Recently, classical results on completeness of trajectories of Hamiltonian systems obtained at the beginning of the seventies, have been revisited, improved and applied to Lorentzian Geometry. Our aim here is threefold: to give explicit…
This article provides a self contained overview of the geometry and dynamics of relativistic brane models, of the category that includes point particle, string, and membrane representations for phenomena that can be considered as being…
We investigate the dynamics of a single deformable self-propelled particle which undergoes a spinning motion in a two-dimensional space. Equations of motion are derived from the symmetry argument for three kinds of variables. One is a…
A new path equation in absolute parallelism (AP) geometry is derived. The equation is a generalization of three path equations derived in a previous work. It can be considered as a geodesic equation modified by a torsion term, whose…
The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…
Given a convex set and an interior point close to the boundary, we prove the existence of a supporting hyperplane whose distance to the point is controlled, in a dimensionally quantified way, by the thickness of the convex set in the…
A new simple geometrical interpretation of complex numbers is presented. It differs from their usual interpretation as points in the complex plane. From the new point of view the complex numbers are rather operations on vectors than points.…