PLANAR MULTIBODY DYNAMICS Formulation, Programming, and Applications. Errata Last update: August 2012

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1 PLANAR MULTIBODY DYNAMICS Formulation, Programming, and Applications Errata Last update: August 202 During the preparation of this tetbook, a great deal of attention was paid to minimize the number of errors that normall occur either in the preparation phase or in the publication phase of a book. Despite that effort, some errors in the manuscript were not detected, as well as other errors that appeared during the publication phase. As such errors become known, the will be reported in this document. This document will be updated as soon as new errors are found. Please refer to the date that appears on the link when ou download, which reflects the date of the last update. The corrections will be listed chronologicall based on their reported dates. This should make it easier for the reader to locate the corrected errors since the last download. A note to the reader: If ou come across an errors, please inform the author b sending an to pen@ .arizona.edu. Thank ou! Page 6; line 5 from the bottom Januar 2009 Change O to B. Attaching a Cartesian reference frame - at B, Page 39; Eample 2.9, 4th line Januar 2009 Replace the second equation with the following equation: Φ 2 = Page 44; Problem 2. Januar 2009 Over-score. appears incorrectl on several Φ s. Make the following changes: In the problem statement: Φ = z + z 2 4z z z 2 (a)... Φ q... (c)... Φ = Φ q q. Page 45; Problem 2.22(a) August 202 Change q = { φ 2 2 to: { } q = φ 2 2 φ 2

2 Page 50; Figure 3.4 Januar 2009 Change the vector component along the -ais from s (ξ) to: s ( ) Page 77; 2nd line Januar 2009 Change Fig. 3.5 to: Fig. 4.3 Page 94; line 3 Januar 2009 % Define spring-damper-actiator constants % Define spring-damper-actuator constants Page 95; equation in the middle of the page Januar 2009 Correct the number in (s,d,a) f = to: (s,d,a) f = Page 99; Equation (4.4), line following equation, and Eq. (4.42) Januar 202 Lambda should be in bold-face: (c) f = D λ (4.4) where λ is an (c) h = D λ (4.42) Page 32; in the middle of the page Januar 2009 Revise the first line of the Jacobian matri in function D to: D = [ jac_j_aq z2 z2 Page 32; near the bottom December 2007 Revise the first line of the MATLAB file to: function gamma = PC_MP_gamma(dees_d) Page 33; near the top Januar 2009 Revise the entries for gamma arra to: gamma = Page 33; near the bottom December 2007 Revise the first and the fourth lines of the MATLAB file to: % file name: PC_FS_A.m % Film Strip Advancer clear all addpath Basics PC_Basics PC_AA Planar Multibod Dnamics: Errata 2

3 Page 36; Figure (d) for Problem 5.3 Januar 2009 The distance b on the figure is misplaced. Replace the figure with the one shown here. b a Page 45; Figure 6.2 Januar 2009 Remove reaction force from (b). O O O (c) f A,B (c ) f B,A A B A B A (a) (b) (c) B Page 48; first line in the first program Januar 2009 % Append to the file P_MP % Append to the file PC_MP Page 49; middle of the page December 2007 Change the MATLAB statement M_diag = to: M = Page 77; second paragraph, first line December 2009 Change joint-coordinate to: point-coordinate Page 26; line 6 in the M-file function Phi = BC_Phi November 2009 Change the line d = r_p{3} - r_p{5}; to: d = r_p{4} - r_p{5}; Page 27; lines & 6 in the M-file function gamma = BC_MP_A_gamma November 2009 Change the line function gamma = BC_MP_A_gamma to: function gamma = BC_gamma Change the line d = r_p{3} - r_p{5}; d_d = r_p_d{3} - r_p_d{5}; to: d = r_p{4} - r_p{5}; d_d = r_p_d{4} - r_p_d{5}; Planar Multibod Dnamics: Errata 3

4 Page 226; Problem 7.9, (a) Januar 2009 Change in term of to in terms of Page 234; middle of the page Januar 202 Change (Eqs. [4.22] to [5.25]) to (Eqs. [4.22] to [5.27]) Page 246; line following Eq. (8.25) Januar 202 Change are the sub-jacobians of to are the transpose of the sub-jacobians of Page 255; Problem 8.8, first line Januar 2009 Change a pin join to a pin joint Page 265; Figure 9.5(b) Januar 202 Add the - aes and the angle φ to the figure: A θ u ξ φ θ 2 ξ 2 Page 266; Equations (9.6) and (9.7) March 202 Both equations require correction. Correct the equations to: r r 0 r 0 φ 0 = θ r 2 r 2 u θ θ 2 r 2 u (9.6) θ 2 φ r B = r (9.7) 2 u 0 0 Planar Multibod Dnamics: Errata 4

5 Page 277; Equation (9.23) November 200 Second and fourth lines have errors. Correct the equation to: * Φ = * Dc + * Dc = * D(B θ + B θ) + * DBθ = D θ + ( * D B + * DB) θ = D θ + D θ = 0 Page 278; Equation (9.25) November 200 The equation is in error. Correct it to: D θ = γ Page 278; Equation (9.26) November 200 First, second and third lines have errors. Correct the equation to: γ = D θ = * D B θ * Dc = * D B θ + * γ Page 298; Last equation March 202 B contains errors. Correct the equation to: r B = r 2 u 0 0 Page 299; Equation (0.9) March 202 This equation contains errors. Correct the equation to: h = B (h M B θ) f + w m r θ r r2 n = 0 0 u 0 f 2 + w 2 m 2 ( r 2 θ + u d2 ) 0 r (f + w m r θ ) + n + r 2 f 2 + w 2 m 2 ( r 2 θ + u d2 ( )) = u f 2 + w 2 m 2 ( ( r 2 θ + u d2 )) (0.9) Page 300; middle of the page December 2007 Change the listed values for h_joint = to: h_joint = Planar Multibod Dnamics: Errata 5

6 Page 324; following the first two lines Januar 202 Change record(:5,:) = to: record(:5,:6) Page 335; Problem.8 December 2007 Change the last line to: (c) Appl the bod coordinate Page 337; Problem.2, fourth line December 2007 Change in Problem.9 to: in Problem.20. Page 344; third line Januar 2009 Change Eqs. (2.6) and (2.9) to: Eqs. (2.6) and (2.9) Page 35; Problem 2., first line December 2007 Change Refer to Problem.3 to: Refer to Problem.4. Page 35; Problem 2.2, first line December 2007 Change Refer to Problem.4 to: Refer to Problem.5. Page 35; Problem 2.3, first line December 2007 Change Refer to Problem.9 to: Refer to Problem.20. Page 35; Problem 2.4, first line December 2007 Change Refer to Problem.20 to: Refer to Problem.2. Page 359; third M-file December 2007 Change the first line of the MATLAB file to: function z_d = E_3_3(t, z) Pages ; the M-file that starts on page December There are several misprint and programming errors in this file. The last two lines that appear on page 367 should be removed. Change the global and the mass matri statements. Add the gravitational constant. There should be no separation line before the % Set time parameters statement. clear all addpath Basics PC_Basics global k_ L 0 d_c_ m_a m_b g r_o M M_arra % Define particle masses and spring-damper characteristics m_a = 3; m_b = 4; ; g = 9.8; k_ = 50; L 0 =.; d_c_ = 20; % Initial velues for coordinates and velocities Planar Multibod Dnamics: Errata 6

7 r_a = [0.5; -]; r_a_d = [0.0; 0.0]; r_o = [0; 0]; r_b = [2; -]; r_b_d = [0.0; 0.0]; % Construct the mass matri (arra) M_arra = [m_a; m_a; m_b; m_b]; M = diag(m_arra); % Initialize z arra z = [r_a; r_b; r_a_d; r_b_d]; % Set time parameters Tspan = [0.0:0.04:.0]; % Integrate [T, zt] = ode45(@e_3_6, Tspan, z); % Animation nt = size(t); plot_trace(nt, r_o, zt) Page 368; the second M-file December 2007 Revise the global statement: function z_d = E_3_6(t, z) global k_ L 0 d_c_ m_a m_b g r_o M M_arra... Page 369; Figure 3.4 December 2007 Due to the errors in the M-file as has been described in Corrections 2 and 3, the figure should be replaced. Page 372; middle of the page December 2007 Add the following short phrase to the end of the paragraph before the M-file function h = BC_h:... b invoking the function BC_radial which is saved in the folder BC_Basics. Page 397; third line of the program November 200 Revise the line c_d = D_all\rhsv; to c_d = [D; D_driver]\rhsv; Planar Multibod Dnamics: Errata 7