By Dan B. Marghitu
Advanced Dynamics: Analytical and Numerical Calculations with MATLAB offers an intensive, rigorous presentation of kinematics and dynamics whereas utilizing MATLAB as an built-in instrument to unravel difficulties. issues provided are defined completely and directly,allowing primary rules to emerge via functions from parts resembling multibody structures, robotics, spacecraft and layout of complicated mechanical units. This booklet differs from others in that it makes use of symbolic MATLAB for either concept and purposes. specified recognition is given to options which are solved analytically and numerically utilizing MATLAB. The illustrations and figures generated with MATLAB strengthen visible studying whereas an abundance of examples supply extra help.
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Extra info for Advanced Dynamics: Analytical and Numerical Calculations with MATLAB
Determine the resultant vector of the system. Numerical application: V1 = 10, V2 = 25, V3 = 15, V4 = 40, A1 (3, 1, 7), A2 (5, −3, 4), A3 (−4, −3, 1), and A4 (4, 2, −3). Solution The magnitudes, Vi , of the vectors Vi and the coordinates, xi , yi , zi , of the points Ai , i = 1, 2, 3, 4 are introduced with MATLAB as V(1)=10; x(1)= 3; x(2)= 5; x(3)=-4; x(4)= 4; V(2)=25; y(1)= 1; y(2)=-3; y(3)=-3; y(4)= 2; V(3)=15; z(1)= 7; z(2)= 4; z(3)= 1; z(4)=-3; V(4)=40; % magnitudes V_i % A_1 % A_2 % A_3 % A_4.
30) for a + b and −b, it results |a| = |(a + b) + (−b)| ≤ |a + b| + |−b| , or |a + b| ≥ |a| − |−b| = |a| − |b| . 33), the following relations can be written: |a| − |b| ≤ |a + b| ≤ |a| + |b| , for |a| > |b| , |b| − |a| ≤ |a + b| ≤ |a| + |b| , for |a| < |b| . 9 Coordinate Transformation Let ı, j and k be the unit vectors of an orthogonal Cartesian reference frame Oxyz and ı , j and k be the unit vectors of an orthogonal Cartesian reference frame Ox y z . 34) where α11 = ı · ı = cos(Ox , Ox), α12 = ı · j = cos(Ox , Oy), α13 = ı · k = cos(Ox , Oz), α21 = j · ı = cos(Oy , Ox), α22 = j · j = cos(Oy , Oy), α23 = j · k = cos(Oy , Oz), α31 = k · ı = cos(Oz , Ox), α32 = k · j = cos(Oz , Oy), α33 = k · k = cos(Oz , Oz) are the direction cosines between unit vectors along the coordinate axes.
590, V2z = 0. 273 k. 778. 220. 8545. 299◦. 3f (deg)\n’, acosd(costheta)) 50 1 Vector Algebra The MATLAB function acos(phi) is the arccosine of the element phi and acosd(phi) is the inverse cosine , expressed in degrees, of the element of phi. Next, the vectors V1 , V2 , R, uR , and V1 × V2 will be plotted using MATLAB. 5*[0 a 0 b 0 c]) grid on, hold on xlabel(’x’), ylabel(’y’), zlabel(’z’) For the default “Cartesian” axes mode, the coordinate system origin is at x=y=0. The x-axis is numbered from left to right, the y-axis is numbered from bottom to top, and the z-axis is vertical with values increasing from bottom to top.
Advanced Dynamics: Analytical and Numerical Calculations with MATLAB by Dan B. Marghitu