Displaying similar documents to “Doubly asymptotic trajectories of Lagrangian systems and a problem by Kirchhoff”

The Lagrange rigid body motion

Tudor Ratiu, P. van Moerbeke (1982)

Annales de l'institut Fourier

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We discuss the motion of the three-dimensional rigid body about a fixed point under the influence of gravity, more specifically from the point of view of its symplectic structures and its constants of the motion. An obvious symmetry reduces the problem to a Hamiltonian flow on a four-dimensional submanifold of s o ( 3 ) × s o ( 3 ) ; they are the customary Euler-Poisson equations. This symplectic manifold can also be regarded as a coadjoint orbit of the Lie algebra of the semi-direct product group S O ( 3 ) × s o ( 3 ) with...

A theorem for rigid motions in Post-Newtonian celestial mechanics.

J.M. Gambi, P. Zamorano, P. Romero, M.L. García del Pino (2003)

RACSAM

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The velocity field distribution for rigid motions in the Born?s sense applied to Post-Newtonian Relativistic Celestial Mechanics is examined together with its compatibility with the Newtonian distribution.

Mechanics

Stefan Banach

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CONTENTS Preface................ III CHAPTER I. THEORY OF VECTORS I. Operations on vectors § 1. Preliminary definitions.................. 1 § 2. Components of a vector.................. 2 § 3. Sum and difference of vectors.................. 3 § 4. Product of a vector by a number.................. 4 § 5. Components of a sum and product.................. 5 § 6. Resolution of a vector.................. 6 § 7. Scalar product.................. 7 § 8. Vector product.................. 9 § 9....

On D’Alembert’s Principle

Larry M. Bates, James M. Nester (2011)

Communications in Mathematics

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A formulation of the D’Alembert principle as the orthogonal projection of the acceleration onto an affine plane determined by nonlinear nonholonomic constraints is given. Consequences of this formulation for the equations of motion are discussed in the context of several examples, together with the attendant singular reduction theory.

Symmetries and currents in nonholonomic mechanics

Michal Čech, Jana Musilová (2014)

Communications in Mathematics

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In this paper we derive general equations for constraint Noethertype symmetries of a first order non-holonomic mechanical system and the corresponding currents, i.e. functions constant along trajectories of the nonholonomic system. The approach is based on a consistent and effective geometrical theory of nonholonomic constrained systems on fibred manifolds and their jet prolongations, first presented and developed by Olga Rossi. As a representative example of application of the geometrical...

On a constrained minimization problem arising in hemodynamics

João Janela, Adélia Sequeira (2008)

Banach Center Publications

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Experimental evidence collected over the years shows that blood exhibits non-Newtonian characteristics such as shear-thinning, viscoelasticity, yield stress and thixotropic behaviour. Under certain conditions these characteristics become relevant and must be taken into consideration when modelling blood flow. In this work we deal with incompressible generalized Newtonian fluids, that account for the non-constant viscosity of blood, and present a new numerical method to handle fluid-rigid...