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Mechanics of Rigid Bodies
Published in Osamu Morita, Classical Mechanics in Geophysical Fluid Dynamics, 2019
The motion of many-particle systems and rigid bodies has two aspects of motion, i.e., the translational motion and the rotational motion. In this chapter, we will limit our discussion to the translational motion. The center of mass is defined as the point at which all mass of many-particle systems or rigid bodies is considered to concentrate. The translation of a center of mass may be described by the equation of motion as it is for a single particle.
Integration 3
Published in C.W. Evans, Engineering Mathematics, 2019
The moment of inertia of a system of particles about an axis is equal to the sum of the moment of inertia of the system about a parallel axis through the centre of mass and the product of the mass of the system with the square of the distance between the two axes.
Case Studies
Published in Nicholas Stergiou, Nonlinear Analysis for Human Movement Variability, 2018
Anastasia Kyvelidou, Leslie M. Decker
Human posture control involves controlling the body’s position in space for two purposes: stability and orientation. Stability, also broadly referred to as balance, is the ability to control the center of mass in relationship to the base of support. Orientation is defined as the ability to maintain an appropriate relationship between the body segments and between the body and the environment (Shumway-Cook and Woollacott 2012). The center of pressure (COP) at the base of support in standing has traditionally been considered a reflection of the organization of posture (Massion 1992). Researchers have utilized the COP in the studies of postural control in adults (Buchanan and Horak 2001; Horak and Macpherson 1996; Newell et al. 1993; Winstein et al. 1989) and children (Horak et al. 1988; Nashner et al. 1983; Odenrick and Sandstedt 1984; Riach and Hayes 1987) developing standing skills. However, there have been conflicting interpretations of the COP data using the standard variables of length of path, excursion in the sagittal or frontal directions, and the area of the path of the COP during stable standing. For example, different researchers have interpreted an increased COP area to suggest greater motor control because the individual can recover from disruptions to posture (Hughes et al. 1996), while others interpret an increased area as a lack of postural control (Riach and Hayes 1987).
The container loading problem with cargo stability: a study on support factors, mechanical equilibrium and grids
Published in Engineering Optimization, 2021
Liliane de Azevedo Oliveira, Vinícius Loti de Lima, Thiago Alves de Queiroz, Flávio Keidi Miyazawa
Assuming that the cargo is in a uniform gravity field, the weight is assumed to be acting on the items' centres of mass. The centre of mass is the point where all masses of an item are considered to be concentrated. As each item is homogeneous, the centre of mass coincides with the item's geometric centre. Additionally, the reaction force of the weight acts as the normal force.