Controlling nonholonomic Chaplygin systems
نویسندگان
چکیده
منابع مشابه
Nonholonomic Hamilton–jacobi Theory via Chaplygin Hamiltonization
We develop Hamilton–Jacobi theory for Chaplygin systems, a certain class of nonholonomic mechanical systems with symmetries, using a technique called Hamiltonization, which transforms nonholonomic systems into Hamiltonian systems. We give a geometric account of the Hamiltonization, identify necessary and sufficient conditions for Hamiltonization, and apply the conventional Hamilton–Jacobi theor...
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This document is a brief overview of the Hamilton-Jacobi theory of Chaplygin systems based on [1]. In this paper, after reducing Chaplygin systems, Ohsawa et al. use a technique that they call Chaplygin Hamiltonization to turn the reduced Chaplygin systems into Hamiltonian systems. This method was first introduced in a paper by Chaplygin in 1911 where he reduced some nonholonomic systems by the...
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The celebrated problem of a non-homogeneous sphere rolling over a horizontal plane was proved to be integrable and was reduced to quadratures by Chaplygin. Applying the formalism of variational integrators (discrete Lagrangian systems) with nonholonomic constraints and introducing suitable discrete constraints, we construct a discretization of the n-dimensional generalization of the Chaplygin s...
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When the generalized velocity of a mechanical system satis es an equality condition that cannot be written as an equivalent condition on the generalized position, the system is called a nonholonomic system [1, 2]. Nonholonomic condition may arise from constraints such as pure rolling of a wheel or from physical conservation laws such as the conservation of angular momentum of a free oating body...
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In this paper we discuss asymptotic stability in energy-preserving systems which have an almost Poisson structure. In particular we consider a class of Poisson systems which includes the Toda lattice. In standard Hamiltonian systems one of course does not expect asymptotic stability. The key here is the structure of the phase space of the Poisson or almost Poisson systems and the nature of the ...
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ژورنال
عنوان ژورنال: Brazilian Journal of Physics
سال: 2010
ISSN: 0103-9733
DOI: 10.1590/s0103-97332010000200002