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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of nonlinear science 6 (1996), S. 271-292 
    ISSN: 1432-1467
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Summary This article concerns the three-dimensional, large deformation dynamics of an inextensible, unshearable rod. To enforce the conditions of inextensibility and unshearability, a technique we call the impetus-striction method is exploited to reformulate the constrained Lagrangian dynamics as an unconstrained Hamiltonian system in which the constraints appear as integrals of the evolution. We show here that this impetus-striction formulation naturally leads to a numerical scheme which respects the constraints and conservation laws of the continuous system. We present simulations of the dynamics of a rod that is fixed at one end and free at the other.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Archive for rational mechanics and analysis 85 (1984), S. 311-354 
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract This paper describes previously unknown stabilities and instabilities of planar equilibrium configurations of a nonlinearly elastic rod that is buckled under the action of a dead-load. The governing equations are derived from variational principles, including ones of isoperimetric type. Properties of stability are accordingly determined by study of the second variation. Stabilities to deformations both in the plane and out of the plane are considered. Among the newly discovered properties are: secondary bifurcation from the first buckled mode, marked differences between stability to two-dimensional and to three-dimensional variations, and the stabilizing influence of resistance to twist. In the isoperimetric examples, the analysis makes crucial use of a novel device to account for the dependence of the second variation on constraints.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Archive for rational mechanics and analysis 99 (1987), S. 301-328 
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is known that when one branch of a simple fold in a bifurcation diagram represents (linearly) stable solutions, the other branch represents unstable solutions. The theory developed here can predict instability of some branches close to folds, without knowledge of stability of the adjacent branch, provided that the underlying problem has a variational structure. First, one particular bifurcation diagram is identified as playing a special role, the relevant diagram being specified by the choice of functional plotted as ordinate. The results are then stated in terms of the shape of the solution branch in this distinguished bifurcation diagram. In many problems arising in elasticity the preferred bifurcation diagram is the loaddisplacement graph. The theory is particularly useful in applications where a solution branch has a succession of folds. The theory is illustrated with applications to simple models of thermal selfignition and of a chemical reactor, both of which systems are of Émden-Fowler type. An analysis concerning an elastic rod is also presented.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Archive for rational mechanics and analysis 135 (1996), S. 357-396 
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A method is presented for deriving unconstrained Hamiltonian systems of partial differential equations equivalent to given constrained Lagrangian systems. The method is applied to the theory of planar, finite-amplitude motions of inextensible and unshearable elastic rods. The constraints of inextensibility and unshearability become integrals of motion in the Hamiltonian formulation. It is known that in the theory of uniform, inextensible, unshearable rods of infinite length there arise solitary-wave solutions with the property that each profile can move at arbitrary speed. The Hamiltonian formulation is exploited to analyze the stability properties of these solitary waves. The wave profiles are first characterized as critical points of an appropriate time-invariant functional. It is then shown that for a certain range of wave speeds the solitary-wave profiles are actually nonisolatedminimizers of the functional, a fact with implications for nonlinear stability.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Celestial mechanics and dynamical astronomy 50 (1990), S. 349-386 
    ISSN: 1572-9478
    Keywords: Hamiltonian mechanics ; relative equilibrium ; rigid body dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper concerns the dynamics of a rigid body of finite extent moving under the influence of a central gravitational field. A principal motivation behind this paper is to reveal the hamiltonian structure of the n-body problem for masses of finite extent and to understand the approximation inherent to modeling the system as the motion of point masses. To this end, explicit account is taken of effects arising because of the finite extent of the moving body. In the spirit of Arnold and Smale, exact models of spin-orbit coupling are formulated, with particular attention given to the underlying Lie group framework. Hamiltonian structures associated with such models are carefully constructed and shown to benon-canonical. Special motions, namely relative equilibria, are investigated in detail and the notion of anon-great circle relative equilibrium is introduced. Non-great circle motions cannot arise in the point mass model. In our analysis, a variational characterization of relative equilibria is found to be very useful. Thereduced hamiltonian formulation introduced in this paper suggests a systematic approach to approximation of the underlying dynamics based on series expansion of the reduced hamiltonian. The latter part of the paper is concerned with rigorous derivations of nonlinear stability results for certain families of relative equilibria. Here Arnold's energy-Casimir method and Lagrange multiplier methods prove useful.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Journal of low temperature physics 96 (1994), S. 245-274 
    ISSN: 1573-7357
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Experimental results are presented for counterflow and isothermal coflow through large-pore porous materials, with porosities greater than 90% and permeabilities of order 10−11 m2. Counterflow velocities ranging from 0.06 to 0.14 m/s were obtained. Because of the large-pore geometry, and the velocity range investigated, the superfluid is fully turbulent. The counterflow data are well described by the two-fluid model using the Schwarz model of homogeneous mutual friction, with a larger, empirically-modified, mutual friction coefficient. The same mutual friction model is applied to the coflow results, assuming that dissipation due to superfluid vortex interaction with the wall of the porous media is negligible. In this case, the normal-fluid and superfluid velocities are coupled through the mutual friction, and relative velocities are calculated from pressure drop measurements. For mass flow velocities in the range 0.00 to 0.10 m/s, we calculate relative velocities up to 0.07 m/s, and normal-fluid velocities in excess of 0.04m/s. An interesting feature of the coflow pressure drop, as a function of the normal-fluid velocity, is that it is larger than the counterflow pressure drop by the ratio of the total density to the normal-fluid density.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Motivation and emotion 9 (1985), S. 1-10 
    ISSN: 1573-6644
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract Subjects were classified according to whether they were high or low in the need for Power and high or low in gain in 3-methoxy-4-hydroxyphenylglycol (MHPG), a putative index of brain norepinephrine (NE) turnover, after engaging in some tasks that involved memory for story content. Subjects who were high inn Power and in the index of brain NE turnover showed better recall of power-related facts than subjects low on both these characteristics, confirming an earlier finding, which suggests that the need for Power is subserved by a noradrenergic reward system in the brain.
    Type of Medium: Electronic Resource
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  • 8
    Publication Date: 2023-08-14
    Language: English
    Type: article , doc-type:article
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