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3-parametric robot manipulator with intersecting axes

Jerzy Gądek (1995)

Applications of Mathematics

A p -parametric robot manipulator is a mapping g of ℝ p into the homogeneous space P = ( C 6 × C 6 ) / Diag ( C 6 × C 6 ) represented by the formula g ( u 1 , u 2 , ⋯ , u p ) = exp ( u 1 X 1 ) · ⋯ · exp ( u p X p ) , where C 6 is the Lie group of all congruences of E 3 and X 1 , X 2 , ⋯ , X p are fixed vectors from the Lie algebra of C 6 . In this paper the 3 -parametric robot manipulator will be expressed as a function of rotations around its axes and an invariant of the motion of this robot manipulator will be given. Most of the results presented here have been obtained during the author’s stay at Charles University in Prague....

A BF-regularization of a nonstationary two-body problem under the Maneff perturbing potential.

Ignacio Aparicio, Luis Floría (1997)

Extracta Mathematicae

The process of transforming singular differential equations into regular ones is known as regularization. We are specially concerned with the treatment of certain systems of differential equations arising in Analytical Dynamics, in such a way that, accordingly, the regularized equations of motion will be free of singularities.

A. C. Clarke's Space Odyssey and Newton's law of gravity

Bartoň, Stanislav, Renčín, Lukáš (2017)

Programs and Algorithms of Numerical Mathematics

In his famous tetralogy, Space Odyssey, A. C. Clarke called the calculation of a motion of a mass point in the gravitational field of the massive cuboid a classical problem of gravitational mechanics. This article presents a proposal for a solution to this problem in terms of Newton's theory of gravity. First we discuss and generalize Newton's law of gravitation. We then compare the gravitational field created by the cuboid -- monolith, with the gravitational field of the homogeneous sphere. This...

A canonical connection on sub-Riemannian contact manifolds

Michael Eastwood, Katharina Neusser (2016)

Archivum Mathematicum

We construct a canonically defined affine connection in sub-Riemannian contact geometry. Our method mimics that of the Levi-Civita connection in Riemannian geometry. We compare it with the Tanaka-Webster connection in the three-dimensional case.

A comparison of two FEM-based methods for the solution of the nonlinear output regulation problem

Branislav Rehák, Sergej Čelikovský, Javier Ruiz, Jorge Orozco-Mora (2009)

Kybernetika

The regulator equation is the fundamental equation whose solution must be found in order to solve the output regulation problem. It is a system of first-order partial differential equations (PDE) combined with an algebraic equation. The classical approach to its solution is to use the Taylor series with undetermined coefficients. In this contribution, another path is followed: the equation is solved using the finite-element method which is, nevertheless, suitable to solve PDE part only. This paper...

A completion of A. Bressan's work on axiomatic foundations of the Mach Painlevé type for various classical theories of continuous media. Part 1. Completion of Bressan's work based on the notion of gravitational equivalence of affine inertial frames

Adriano Montanaro (1987)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The work [3], where various classical theories on continuous bodies are axiomatized from the Mach-Painlevè point of view, is completed here in two alternative ways; in that work, among other things, affine inertial frames are defined within classical kinematics. Here, in Part I, a thermodynamic theory of continuous bodies, in which electrostatic phenomena are not excluded, is dealt with. The notion of gravitational equivalence among affine inertial frames and the notion of gravitational isotropy...

A continuation method for motion-planning problems

Yacine Chitour (2006)

ESAIM: Control, Optimisation and Calculus of Variations

We apply the well-known homotopy continuation method to address the motion planning problem (MPP) for smooth driftless control-affine systems. The homotopy continuation method is a Newton-type procedure to effectively determine functions only defined implicitly. That approach requires first to characterize the singularities of a surjective map and next to prove global existence for the solution of an ordinary differential equation, the Wazewski equation. In the context of the MPP, the aforementioned...

A continuation method for motion-planning problems

Yacine Chitour (2005)

ESAIM: Control, Optimisation and Calculus of Variations

We apply the well-known homotopy continuation method to address the motion planning problem (MPP) for smooth driftless control-affine systems. The homotopy continuation method is a Newton-type procedure to effectively determine functions only defined implicitly. That approach requires first to characterize the singularities of a surjective map and next to prove global existence for the solution of an ordinary differential equation, the Wazewski equation. In the context of the MPP, the aforementioned...

A discrete contact model for crowd motion

Bertrand Maury, Juliette Venel (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The aim of this paper is to develop a crowd motion model designed to handle highly packed situations. The model we propose rests on two principles: we first define a spontaneous velocity which corresponds to the velocity each individual would like to have in the absence of other people. The actual velocity is then computed as the projection of the spontaneous velocity onto the set of admissible velocities (i.e. velocities which do not violate the non-overlapping constraint). We describe here the...

A discrete contact model for crowd motion

Bertrand Maury, Juliette Venel (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

The aim of this paper is to develop a crowd motion model designed to handle highly packed situations. The model we propose rests on two principles: we first define a spontaneous velocity which corresponds to the velocity each individual would like to have in the absence of other people. The actual velocity is then computed as the projection of the spontaneous velocity onto the set of admissible velocities (i.e. velocities which do not violate the non-overlapping constraint). We describe here...

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