China
Africa
Explore chapters and articles related to this topic
Fundamentals of Elasto-Plastic Mechanics
Published in Yichun Zhou, Li Yang, Yongli Huang, Micro- and MacroMechanical Properties of Materials, 2013
Yichun Zhou, Li Yang, Yongli Huang
are the cosines between the normal direction of the oblique plane, ν, and the unit vectors of the coordinates axes, ei, called direction cosines. Suppose the area of the oblique plane △ABC is d S. Then the areas of three negative planes are as follows () dS1=the area of△PBC=v1dS,dS2=the area of△PCA=v2dS,dS3=the area of△PAB=v3dS.
System Modelling
Published in Richard Leach, Stuart T. Smith, Basics of Precision Engineering, 2017
Direction cosines are defined as the cosine of the angle between an arbitrary position vector and each of the axes of the base coordinate system. Figure 8.5 shows an arbitrary position vector v and the angles relative to the base coordinate system, where a is the angle between the vector v and the x-axis, b is the angle between the vector v and the y-axis and c is the angle between the vector v and the z-axis. The direction cosines are then given by
Reflection and Refraction of Electromagnetic Waves
Published in Ahmad Shahid Khan, Saurabh Kumar Mukerji, Electromagnetic Fields, 2020
Ahmad Shahid Khan, Saurabh Kumar Mukerji
The direction cosines are the cosines of angles which the unit vectors make with the three axes. In Equation 17.1b: n∨·r∨=xcosA+ycosB+zcosC
The temperature dependence of the helical pitch in a cholesteric liquid crystal
Published in Molecular Physics, 2021
Robert A. Skutnik, Jan-Christoph Eichler, Marco G. Mazza, Martin Schoen
Another quantity of interest is the orientation distribution function (odf). As explained in detail in Refs. [30,32] it is advantageous to rotate the orientations of the mesogens in the - and in the off-lattice model such that they lie in the x−y plane with their tips located on the equator of the unit sphere . Because the eigensystem of consists of three vectors that are initially not necessarily orthogonal to the equatorial plane of the sphere, a rotation of the orientations of the mesogens is needed. The rotation is effected by a rotation matrix which can be set up as a direction cosine matrix between vectors of the standard basis and components of the three eigenvectors .
Modeling the effects of musculoskeletal geometry on scapulohumeral muscle moment arms and lines of action
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2019
Daanish M. Mulla, Joanne N. Hodder, Monica R. Maly, James L. Lyons, Peter J. Keir
Model-predicted moment arms and lines of action were quantified throughout scapular plane arm elevation. The upper extremity was postured in a series of static thoracohumeral (HT) elevation angles from 15° to 120° at 5° intervals based on available data (Ludewig et al. 2009). Moment arms were quantified using the tendon excursion method at the GH joint: elevation/depression, horizontal adduction/abduction, and internal/external rotation (positive directions italicized). Lines of action were computed as the unit vector direction cosine of the muscle pathway from humeral to scapula attachment (or clavicle for the anterior deltoid) defined in the scapula coordinate system (Supplementary Figure A1). For muscle pathways directed around wrapping objects, the vector was calculated from the scapula to the first path point at the humerus (i.e. ‘effective’ insertion). Lines of action in the superior–inferior (LOAS-I) and anterior-posterior (LOAA-P) directions were calculated as the angle clockwise to the Z-axis in the YZ and XZ planes, respectively.
Improved Finite Volume Method for Three-Dimensional Radiative Heat Transfer in Complex Enclosures Containing Homogenous and Inhomogeneous Participating Media
Published in Heat Transfer Engineering, 2018
Kamel Guedri, Abdulmajeed Saeed Al-Ghamdi
In these equations, Ile, Iln and Ilt represent the radiation intensities on the downstream interfaces in the direction, ΔΩl. However, Ilw, Ils and Ilb are those on the upstream interfaces in the same direction (Figure 1b). The west, east, south, north, bottom and top surfaces of the control volume, VP, are denoted by the subscripts, w, e, s, n, b, and t, respectively (Figure 1b). L and Ai represents the total number of discrete solid angles and the area of the control-volume face i, respectively. The term Nli, is evaluated analytically by Eq. (6). It takes into account the variation of the intensity direction within ΔΩl, while the intensity magnitude is assumed constant. Thus it represents the direction cosine integrated over the control angle ΔΩl. This formulation is the same as presented by Chai et al. [17, 19, 20], Borjini et al. [11] and Guedri et al. [12, 14,15]. However, others researchers did not divide the direction cosine by the control angle and they used in their formulations [2,3,5–10].