Topic
Holonomic constraints
About: Holonomic constraints is a research topic. Over the lifetime, 1106 publications have been published within this topic receiving 36268 citations.
Papers published on a yearly basis
Papers
More filters
••
TL;DR: In this paper, a numerical algorithm integrating the 3N Cartesian equations of motion of a system of N points subject to holonomic constraints is formulated, and the relations of constraint remain perfectly fulfilled at each step of the trajectory despite the approximate character of numerical integration.
18,394 citations
••
TL;DR: In this paper, the authors derived new holonomicq-difference equations for the matrix coefficients of the products of intertwining operators for quantum affine algebra representations of levelk.
Abstract: We derive new holonomicq-difference equations for the matrix coefficients of the products of intertwining operators for quantum affine algebra
representations of levelk. We study the connection opertors between the solutions with different asymptotics and show that they are given by products of elliptic theta functions. We prove that the connection operators automatically provide elliptic solutions of Yang-Baxter equations in the “face” formulation for any type of Lie algebra
$$\mathfrak{g}$$
and arbitrary finite-dimensional representations of
. We conjecture that these solutions of the Yang-Baxter equations cover all elliptic solutions known in the contexts of IRF models of statistical mechanics. We also conjecture that in a special limit whenq→1 these solutions degenerate again into
solutions with
$$q' = \exp \left( {\frac{{2\pi i}}{{k + g}}} \right)$$
. We also study the simples examples of solutions of our holonomic difference equations associated to
$$U_q (\widehat{\mathfrak{s}\mathfrak{l}(2)})$$
and find their expressions in terms of basic (orq−)-hypergeometric series. In the special case of spin −1/2 representations, we demonstrate that the connection matrix yields a famous Baxter solution of the Yang-Baxter equation corresponding to the solid-on-solid model of statistical mechanics.
683 citations
••
TL;DR: In this article, it was shown that any identity involving sums and integrals of products of holonomic functions can be verified in a finite number of steps. But this is partially substantiated by an algorithm that proves terminating hypergeometric series identities, and that is given both in English and in MAPLE.
595 citations
•
14 Feb 2005TL;DR: Geometric integrators as mentioned in this paper are time-stepping methods, designed such that they exactly satisfy conservation laws, symmetries or symplectic properties of a system of differential equations.
Abstract: Geometric integrators are time-stepping methods, designed such that they exactly satisfy conservation laws, symmetries or symplectic properties of a system of differential equations. In this book the authors outline the principles of geometric integration and demonstrate how they can be applied to provide efficient numerical methods for simulating conservative models. Beginning from basic principles and continuing with discussions regarding the advantageous properties of such schemes, the book introduces methods for the N-body problem, systems with holonomic constraints, and rigid bodies. More advanced topics treated include high-order and variable stepsize methods, schemes for treating problems involving multiple time-scales, and applications to molecular dynamics and partial differential equations. The emphasis is on providing a unified theoretical framework as well as a practical guide for users. The inclusion of examples, background material and exercises enhance the usefulness of the book for self-instruction or as a text for a graduate course on the subject.
498 citations
01 Jan 2004
TL;DR: Geometric integrators as mentioned in this paper are time-stepping methods, designed such that they exactly satisfy conservation laws, symmetries or symplectic properties of a system of differential equations.
Abstract: Geometric integrators are time-stepping methods, designed such that they exactly satisfy conservation laws, symmetries or symplectic properties of a system of differential equations. In this book the authors outline the principles of geometric integration and demonstrate how they can be applied to provide efficient numerical methods for simulating conservative models. Beginning from basic principles and continuing with discussions regarding the advantageous properties of such schemes, the book introduces methods for the N-body problem, systems with holonomic constraints, and rigid bodies. More advanced topics treated include high-order and variable stepsize methods, schemes for treating problems involving multiple time-scales, and applications to molecular dynamics and partial differential equations. The emphasis is on providing a unified theoretical framework as well as a practical guide for users. The inclusion of examples, background material and exercises enhance the usefulness of the book for self-instruction or as a text for a graduate course on the subject.
438 citations