Formulation and performance of variational integrators for rotating bodies

Variational integrators are obtained for two mechanical systems whose configuration spaces are, respectively, the rotation group and the unit sphere. In the first case, an integration algorithm is presented for Euler’s equations of the free rigid body, following the ideas of Marsden et al. (Nonlinearity 12:1647–1662, 1999). In the second example, a variational time integrator is formulated for the rigid dumbbell. Both methods are formulated directly on their nonlinear configuration spaces, without using Lagrange multipliers. They are one-step, second order methods which show exact conservation of a discrete angular momentum which is identified in each case. Numerical examples illustrate their properties and compare them with existing integrators of the literature

Simulating the effect of high-intensity sound on cetaceans: Modeling approach and a case study for Cuvier’s beaked whale ( Ziphius cavirostris

A finite element model is formulated to study the steady-state vibration response of the anatomy of a whale (Cetacea) submerged in seawater. The anatomy was reconstructed from a combination of two-dimensional (2D) computed tomography (CT) scan images, identification of Hounsfield units with tissue types, and mapping of mechanical properties. A partial differential equation model describes the motion of the tissues within a Lagrangean framework. The computational model was applied to the study of the response of the tissues within the head of a neonate Cuvier's beaked whale Ziphius cavirostris. The characteristics of the sound stimulus was a continuous wave excitation at 3500 Hz and 180 dB re: 1 mu Pa received level, incident as a plane wave. We model the beaked whale tissues embedded within a volume of seawater. To account for the finite dimensions of the computational volume, we increased the damping for viscous shear stresses within the water volume, in an attempt to reduce the contribution of waves reflected from the boundaries of the computational box. The mechanical response of the tissues was simulated including: strain amplitude; dissipated power; and pressure. The tissues are not likely to suffer direct mechanical or thermal damage, within the range of parameters tested. (c) 2006 Acoustical Society of America