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Application of a center manifold theory to a reaction-diffusion system of collective motion of camphor disks and boats

Shin-Ichiro Ei, Kota Ikeda, Masaharu Nagayama, Akiyasu Tomoeda (2014)

Mathematica Bohemica

Unidirectional motion along an annular water channel can be observed in an experiment even with only one camphor disk or boat. Moreover, the collective motion of camphor disks or boats in the water channel exhibits a homogeneous and an inhomogeneous state, depending on the number of disks or boats, which looks like a kind of bifurcation phenomena. In a theoretical research, the unidirectional motion is represented by a traveling wave solution in a model. Hence it suffices to investigate a linearized...

Application of a second order VSC to nonlinear systems in multi-input parametric-pure-feedback form

Antonella Ferrara, Luisa Giacomini (2000)

Kybernetika

The use of a multi-input control design procedure for uncertain nonlinear systems expressible in multi-input parametric-pure feedback form to determine the control law for a class of mechanical systems is described in this paper. The proposed procedure, based on the well-known backstepping design technique, relies on the possibility of extending to multi-input uncertain systems a second order sliding mode control approach recently developed, thus reducing the computational load, as well as increasing...

Applications of Lie systems in quantum mechanics and control theory

José F. Cariñena, Arturo Ramos (2003)

Banach Center Publications

Some simple examples from quantum physics and control theory are used to illustrate the application of the theory of Lie systems. We will show, in particular, that for certain physical models both of the corresponding classical and quantum problems can be treated in a similar way, may be up to the replacement of the Lie group involved by a central extension of it. The geometric techniques developed for dealing with Lie systems are also used in problems of control theory. Specifically, we will study...

Applicazioni del teorema di Nekhoroshev alla meccanica celeste

Giancarlo Benettin (2001)

Bollettino dell'Unione Matematica Italiana

The application of Nekhoroshev theory to selected physical systems, interesting for Celestial Mechanics, is here reviewed. Applications include the stability of motions in the weakly perturbed Euler-Poinsot rigid body and the stability of the so-called Lagrangian equilibria L 4 , L 5 in the spatial circular restricted three-body problem. The difficulties to be overcome, which require a nontrivial extension of the standard Nekhoroshev theorem, are the presence of singularities in the fiber structure...

Approximation of Jacobian inverse kinematics algorithms

Krzysztof Tchoń, Joanna Karpińska, Mariusz Janiak (2009)

International Journal of Applied Mathematics and Computer Science

This paper addresses the synthesis problem of Jacobian inverse kinematics algorithms for stationary manipulators and mobile robots. Special attention is paid to the design of extended Jacobian algorithms that approximate the Jacobian pseudoinverse algorithm. Two approaches to the approximation problem are developed: one relies on variational calculus, the other is differential geometric. Example designs of the extended Jacobian inverse kinematics algorithm for 3DOF manipulators as well as for the...

Approximation of solutions of Hamilton-Jacobi equations on the Heisenberg group

Yves Achdou, Italo Capuzzo-Dolcetta (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

We propose and analyze numerical schemes for viscosity solutions of time-dependent Hamilton-Jacobi equations on the Heisenberg group. The main idea is to construct a grid compatible with the noncommutative group geometry. Under suitable assumptions on the data, the Hamiltonian and the parameters for the discrete first order scheme, we prove that the error between the viscosity solution computed at the grid nodes and the solution of the discrete problem behaves like h where h is the mesh step. Such...

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