TAILIEUCHUNG - Mechanics.Of.Materials.Saouma Episode 2

Tham khảo tài liệu ' episode 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 3 ra Figure Direction Cosines Vectors 8 A vector is a directed line segment which can denote a variety of quantities such as position of point with respect to another position vector a force or a traction. 9 A vector may be defined with respect to a particular coordinate system by specifying the components of the vector in that system. The choice of the coordinate system is arbitrary but some are more suitable than others axes corresponding to the major direction of the object being analyzed . 10 The rectangular Cartesian coordinate system is the most often used one others are the cylindrical spherical or curvilinear systems . The rectangular system is often represented by three mutually perpendicular axes Oxyz with corresponding unit vector triad i j k or ei e2 e3 such that ixj k jxk i kxi j i-i j-j k-k 1 i-j j-k k-i 0 Such a set of base vectors constitutes an orthonormal basis. 11 An arbitrary vector v may be expressed by v vxi v yj vz k where vx v-i v cos a vy v-j v cos 3 vz v-k v cos Y are the projections of v onto the coordinate axes Fig. . 12 The unit vector in the direction of v is given by ev cos ai cos 3j cos yk Victor Saouma Mechanics of Materials II MATHEMATICAL PRELIMINARIES Part I Vectors and Tensors I Since v is arbitrary it follows that any unit vector will have direction cosines of that vector as its Cartesian components. 13 The length or more precisely the magnitude of the vector is denoted by II v 11 Ự 2 2 2. 14 fWe will denote the contravariant components of a vector by superscripts vk and its covariant components by subscripts vk the significance of those terms will be clarified in Sect. . Operations 15 Addition of two vectors a b is geometrically achieved by connecting the tail of the vector b with the head of a Fig. . Analytically the sum vector will have components _ a1 b1 a2 b2 a3 b3 J. b a 0 a b Figure Vector Addition 16 Scalar multiplication aa will scale .

TỪ KHÓA LIÊN QUAN
Đã phát hiện trình chặn quảng cáo AdBlock
Trang web này phụ thuộc vào doanh thu từ số lần hiển thị quảng cáo để tồn tại. Vui lòng tắt trình chặn quảng cáo của bạn hoặc tạm dừng tính năng chặn quảng cáo cho trang web này.