By Dan B. Marghitu

ISBN-10: 1461434742

ISBN-13: 9781461434740

*Advanced Dynamics: Analytical and Numerical Calculations with MATLAB* offers a radical, rigorous presentation of kinematics and dynamics whereas utilizing MATLAB as an built-in software to unravel difficulties. issues provided are defined completely and directly,allowing primary ideas to emerge via functions from components comparable to multibody structures, robotics, spacecraft and layout of advanced mechanical units. This booklet differs from others in that it makes use of symbolic MATLAB for either conception and functions. distinct realization is given to ideas which are solved analytically and numerically utilizing MATLAB. The illustrations and figures generated with MATLAB make stronger visible studying whereas an abundance of examples provide extra aid.

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**Extra info for Advanced Dynamics: Analytical and Numerical Calculations with MATLAB**

**Example text**

Color’,’k’,’LineWidth’,1) quiver3(0,0,0, rB(1),rB(2),rB(3),1,... ’Color’,’k’,’LineWidth’,1) where the statement quiver3(x,y,z,u,v,w) represents a vector as an arrow at the point (x,y,z) with the components (u,v,w). The dashed line (--) between the points A and B is plotted with the command line([rA(1) rB(1)],[rA(2) rB(2)],[rA(3) rB(3)],... ’LineStyle’,’--’) and the unit vector u is represented with quiver3(... rA(1),rA(2),rA(3), u_ABn(1),u_ABn(2),u_ABn(3),... 3,... 3,... ’r_B’,’fontsize’,14,’fontweight’,’b’) text(...

String’,’ \bf q’,... ’Position’,[q_xn,q_yn,q_zn],... ’FontSize’,14) text(’Interpreter’,’latex’,... ’String’,’ \bf p’,... ’Position’,[p_xn,p_yn,p_zn],... ’FontSize’,14) text(’Interpreter’,’latex’,... ’String’,’ {\bf p}$\times${\bf q}’,... 5,vn(2),vn(3)],... ’FontSize’,14) text(’Interpreter’,’latex’,’String’,’ $O$’,... 5],’FontSize’,14,... ’HorizontalAlignment’,’right’) The MATLAB drawing of the vectors is shown in Fig. 17b. 6. Compute a · (b × c), (a × b) · c and (c × b) · a where a = ax ı + ay j + az k, b = bx ı + by j + bz k, and c = cx ı + cy j + cz k.

10 Tensors Let Oxyz and Ox y z be two sets of rectangular Cartesian reference frames. 45) as Xi = 3 ∑ αi j X j j=1 and Xi = 3 ∑ αi j X j , where i = 1, 2, 3. 53) where Xk (k = 1, 2, 3) are the components of a vector X. There are nine scalars X11 , X12 , X13 , X21 , X22 , X23 , X31 , X32 , and X33 . A vector defined in the Euclidean space has three components and is called a tensor of rank one. A tensor of rank two, in a Cartesian reference frame Oxyz, is a mathematical entity with nine components Xi j (i = 1, 2, 3 and j = 1, 2, 3).

### Advanced Dynamics: Analytical and Numerical Calculations with MATLAB by Dan B. Marghitu

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