Rotary inertia

About: Rotary inertia is a research topic. Over the lifetime, 2685 publications have been published within this topic receiving 57922 citations.

Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Theory

Abstract: The description of a beam element by only the displacement of its centerline leads to some difficulties in the representation of the torsion and shear effects. For instance such a representation does not capture the rotation of the beam as a rigid body about its own axis. This problem was circumvented in the literature by using a local coordinate system in the incremental finite element method or by using the multibody floating frame of reference formulation. The use of such a local element coordinate system leads to a highly nonlinear expression for the inertia forces as the result of the large element rotation. In this investigation, an absolute nodal coordinate formulation is presented for the large rotation and deformation analysis of three dimensional beam elements. This formulation leads to a constant mass matrix, and as a result, the vectors of the centrifugal and Coriolis forces are identically equal to zero. The formulation presented in this paper takes into account the effect of rotary inertia, torsion and shear, and ensures continuity of the slopes as well as the rotation of the beam cross section at the nodal points. Using the proposed formulation curved beams can be systematically modeled.

The Vibration‐Rotation Energy Levels of Polyatomic Molecules I. Mathematical Theory of Semirigid Asymmetrical Top Molecules

Abstract: The exact classical kinetic energy for a system of point masses is obtained. From this the correct form for the quantum‐mechanical Hamiltonian operator is derived. If the assumption of small vibrations is applied to this operator, the familiar approximation of a rigid top plus normal coordinate vibrator is obtained. In order to secure better approximations, in which larger amplitudes of vibration are admitted, a perturbation method is introduced which permits the change of moment of inertia with vibration, the coupling of rotation and vibration, and the centrifugal stretching effects to be taken into account. If the stretching terms alone are neglected, it is possible to reduce the secular equation for the rotational energy levels to the Wang form, except that ``effective moments of inertia'' must be used whose magnitude depends on the vibrational quantum state. The relation of these quantities to the equilibrium moments of inertia or to the instantaneous moments of inertia averaged over the vibrational motion is not simple, although the numerical deviation from them may not be great. In addition, for molecules with less than orthorhombic symmetry there is the further possibility that the orientation of the principal axes of inertia will vary with the vibrational quantum number. It is also pointed out that the Wang equation should not fit the data when a nearby vibrational state perturbs the state under examination or when the centrifugal effects are large. A method is indicated whereby the latter terms may in principle be calculated.

Inertia and Transformation

Abstract: In this article I argue that strategy scholars have incorrectly borrowed from economists the assumption of organizational plasticity. Particularly in large firms, inertia, rather than plasticity, is the norm. Unfortunately, there can be no simple theory of inertia as its causes are multiple and varied. After sketching out the shapes of the most important sources of inertia, I turn to the problem of overcoming inertia—the question of organizational transformation. Starting with a simple model of organizational capabilities as existing on two levels (unit-based and rooted in coordination among units), I draw some preliminary conclusions about the shape of organizational transformation. In particular, I focus on the interplay between incentive intensity and coordinative capacity and argue that most transformations move through a sequence of phases in which coordinative capacity is first dramatically reduced and then rebuilt along new lines.