Advanced Dynamics: Analytical and Numerical Calculations - download pdf or read online

By Dan B. Marghitu

ISBN-10: 1461434742

ISBN-13: 9781461434740

Advanced Dynamics: Analytical and Numerical Calculations with MATLAB offers an intensive, rigorous presentation of kinematics and dynamics whereas utilizing MATLAB as an built-in software to unravel difficulties. themes offered are defined completely and directly,allowing primary rules to emerge via functions from parts akin to multibody platforms, robotics, spacecraft and layout of complicated mechanical units. This publication differs from others in that it makes use of symbolic MATLAB for either concept and functions. unique recognition is given to suggestions which are solved analytically and numerically utilizing MATLAB. The illustrations and figures generated with MATLAB toughen visible studying whereas an abundance of examples supply extra help.

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13a, the rectangular component of the vector F on the OA direction is f, with the magnitude |f| = f . The vector F acts at an angle β with the positive direction of the x-axis. Find the magnitude |F| = F of the vector F. Numerical application: f =20, α = 30◦ , and β = 60◦ . b 20 18 16 14 F y 12 F y a 10 A θ f 8 6 f 4 α β O Fig. 11 Examples 37 Solution The component of F on the OA direction is |F| cos θ = f . From Fig. 13, the angle θ of the vector F with the OA direction is θ = β − α = 60◦ −30◦ = 30◦.

Pz = |p| sin θ = p sin θ = 5 2 2 The components qx , qy ,and qz of the vector q are qx = q = 4, qy = 0 and qz = 0. 11 Examples 53 It results v = p × q = (py qz − pz qy ) ı + (pz qx − px qz ) j + (px qy − py qx ) k √ √ 5 5 3 5 5 3 (4) − (0) j + (0) − 0 (4) k = 0(0) − (0) ı + 2 2 2 2 = 5 (4)j = 10j. 2 The MATLAB program for the cross product v = p × q is syms p q theta real p_x = p*cos(theta); p_y = 0; p_z = p*sin(theta); q_x = q; q_y = 0; q_z = 0; v = cross([p_x p_y p_z],[q_x q_y q_z]); slist = {p, q, theta}; nlist = {5, 4, pi/6}; vn = subs(v, slist, nlist); fprintf(’p x q = ’) fprintf(’[%s %s %s]’,char(v(1)),char(v(2)),char(v(3))) fprintf(’ = [%g %g %g] \n’, vn) and the output is p x q = [0 p*sin(theta)*q 0] = [0 10 0] The function char(x) converts the array x into MATLAB character array.

0 0 1 ⇒ ⇒ The transpose of the tensor Z given as ⎡ ⎤ Z11 Z21 Z31 Z = ⎣ Z12 Z22 Z32 ⎦ . Z13 Z23 Z33 ⇒ ⇒ ⇒T is obtained by interchanging the subscripts of each element. If Z = Z , the tensor ⇒ Z is called a symmetric tensor. ⇒ ⇒ Two tensors Z and W are added: ⎡ ⎤ Z11 + W11 Z12 + W12 Z13 + W13 Z + W= ⎣ Z21 + W21 Z22 + W22 Z23 + W32 ⎦ Z31 + W31 Z32 + W32 Z33 + W33 ⇒ ⇒ or multiplied by scalars ⎡ ⎤ sZ11 sZ21 sZ31 s Z = ⎣ sZ12 sZ22 sZ32 ⎦ . sZ13 sZ23 sZ33 ⇒ The magnitude of a tensor is defined as ⇒ |Z|= 1 ∑ Zi2j .

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


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