By Jaynie Aydin
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1) The functions Uk := U· d k and Vk := rs . d k are the strains for our theory. An inequality relating V3, U1, U2, which depends on the cross-sectional shape, ensures that material cross sections do not intersect. It is handled by the methods of Sect. 2. Let n(s, t) and m(s, t) denote the contact force and contact couple acting across section s at time t. 3) where pJpq are the components of a positive-definite matrix determined by the mass moments of inertia of the cross sections, Wq := W· d q, and we use the summation convention.
When the viscosity is large, a single complex conjugate pair of eigenvalues, corresponding to a fundamental oscillatory mode, cross the imaginary axis as c is reduced to 0 from a starting value above vo, and stay thereafter in the right half plane. All other eigenvalues stay in the left half plane. If the viscosity is small, then the eigenvalues for the fundamental mode have the same behavior, but several other pairs of eigenvalues cross the imaginary axis from left to right and then cross back again from right to left, staying thereafter in the left half plane.
Even earlier, McKean (1967) has also studied the dynamics of systems in which the entire system configuration influences parametrization. 1) are discussed in Hesse and Tory (1996). For experimental evidence supporting the model, see Tory and Hesse (1996) and Hesse and Ramos (1994). 1) may also be viewed as resulting from the general, twostage, modelling procedure introduced in Hesse (1998). We explain this briefly. At stage one, the main influences on incremental particle velocity evolution are identified (here friction, buoyancy, gravity and molecular diffusion) and used to set up a system of stochastic differential equations for particle motion.
Aisha Ali and the Art of Presenting Dance on Film: An Ethnochoreological Approach (Phd Thesis) by Jaynie Aydin