PLANAR MULTIBODY DYNAMICS Formulation, Programming, and Applications. Errata Last update: November 2014

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1 PLANAR MULTIBODY DYNAMICS Formulation, Programming, and Applications Errata Last update: November 204 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. 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 Change O to B. Attaching a Cartesian reference frame - at B, Page 39; Eample 2.9, 4th line Replace the second equation with the following equation: Φ 2 = Page 44; Problem 2. 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) Change q = { φ 2 2 to: { } q = φ 2 2 φ 2 Page 50; Figure 3.4 Change the vector component along the -ais from s (ξ) to: s () Page 77; 2nd line Change Fig. 3.5 to: Fig. 4.3

2 Page 94; line 3 % Define spring-damper-actiator constants % Define spring-damper-actuator constants Page 95; equation in the middle of the page 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) 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 Revise the first line of the Jacobian matri in function D to: D = [ jac_j_aq z2 z2 Page 32; near the bottom Revise the first line of the MATLAB file to: function gamma = PC_MP_gamma(dees_d) Page 33; near the top Revise the entries for gamma arra to: gamma = Page 33; near the bottom 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 Page 36; Figure (d) for Problem 5.3 The distance b on the figure is misplaced. Replace the figure with the one shown here. b a Planar Multibod Dnamics: Errata 2

3 Page 45; Figure 6.2 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 % Append to the file P_MP % Append to the file PC_MP Page 49; middle of the page Change the MATLAB statement M_diag = to: M = Page 77; second paragraph, first line Change joint-coordinate to: point-coordinate Page 26; line 6 in the M-file function Phi = BC_Phi 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 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}; Page 226; Problem 7.9, (a) Change in term of to in terms of Page 234; middle of the page Change (Eqs. [4.22] to [5.25]) to (Eqs. [4.22] to [5.27]) Page 246; line following Eq. (8.25) Change are the sub-jacobians of to are the transpose of the sub-jacobians of Planar Multibod Dnamics: Errata 3

4 Page 25; Matri before Section 8.4 REMARKS Change the sign of one of the entries in the last column of the Jacobian transpose λ 0.25 λ λ λ 4 0 Page 255; Problem 8.8, first line Change a pin join to a pin joint Page 265; Figure 9.5(b) 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) Both equations require correction. Correct the equations to: r r 0 r 0 r 0 φ 0 = θ r 2 r 2 u θ θ 2 r 2 u (9.6) B = 0 0 θ 2 (9.7) r 2 u φ Page 277; Equation (9.23) 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 Planar Multibod Dnamics: Errata 4

5 Page 278; Equation (9.25) The equation is in error. Correct it to: D θ = γ Page 278; Equation (9.26) First, second and third lines have errors. Correct the equation to: γ = D θ = * D B θ * Dc = * D B θ + * γ Page 286; Equation (9.37) Missing dots. Correct the equation to: θ A A γ = D θ = r u 2 r 2 θ 2 θ 3 Page 298; Last equation B contains errors. Correct the equation to: r B = r 2 u 0 0 Page 299; Equation (0.9) 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 Change the listed values for h_joint = to: h_joint = Page 324; following the first two lines Change record(:5,:) = to: record(:5,:6) Planar Multibod Dnamics: Errata 5

6 Page 335; Problem.8 Change the last line to: (c) Appl the bod coordinate Page 337; Problem.2, fourth line Change in Problem.9 to: in Problem.20. Page 344; third line Change Eqs. (2.6) and (2.9) to: Eqs. (2.6) and (2.9) Page 35; Problem 2., first line Change Refer to Problem.3 to: Refer to Problem.4. Page 35; Problem 2.2, first line Change Refer to Problem.4 to: Refer to Problem.5. Page 35; Problem 2.3, first line Change Refer to Problem.9 to: Refer to Problem.20. Page 35; Problem 2.4, first line Change Refer to Problem.20 to: Refer to Problem.2. Page 359; third M-file 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 367 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 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) Planar Multibod Dnamics: Errata 6

7 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 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 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 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 Revise the line c_d = D_all\rhsv; to c_d = [D; D_driver]\rhsv; Planar Multibod Dnamics: Errata 7