These corrections will bring the 4^{th} and 5^{th} printings to the contents of the 6^{th} printing.
Special thanks to Ralf Kissman for many of the corrections.
It is interesting that although contributions have been made by many, there has been almost zero overlap of their corrections and suggestions. All updates will be posted on a separate page.
There will not be changes in any printing after the 6th. Changes to the 6th and later printings will only appear on the Web.
Additional corrections to the 6th printing are listed in a separate file.
page #

where

correction

cover

Comment on the cover figure  The cover figure shows the motion of a particle around a central force source. There are two central forces acting; an attractive force proportional to 1/r^{3} and a repulsive force proportional to 1/r^{4}. The figure was probably inspired by the hard core repulsive nuclear force. Another possibility, which is computationly simpler is to make the attractive force 1/r^{2} and the repulsive force 1/r^{3}. 
xi

add 2 paragraphs (first and second new on page)  We thank E. Barreto, P. M. Brown, C. Chien, C. Chou, F. Du, R. F. Gans, I. R. Gatland, C. G. Gray, E.J. Guala, Jr., S. Gutti, D. H. Hartman, M. Horbatsch, J. Howard, K. Jagannathan, R. Kissman, L. Kramer, O. Lehtonen, N. A. Lemos, J. Palacios, R. E. Reynolds, D. V. Sathe, G. T, Seidler, J. Suzuki, A. TenneSens, J. Williams. We also thank Martin Tiersten for pointing out the problems with Fig. 3.7 (description) and 3.13 (misleading figure). 
2

10th line above (1.7)  ...inertial system (or inertial frame) by... 
7

title of figure 1.2  ...vector r_{ij}... 
9  integrand of left side of eq. after Eq(1.29)  F_{i} ds_{i} 
13  lhs of first of eqs (1.38)  r_{1} 
14  4^{th }line above second paragraph  ...may be invoked to serve 
15  equations above (1.39)  add "," after first of pair 
15  3rd line after (1.39)  replace word "perfect" with "exact" 
17  Eq. (1.42)  last F should be f 
20  Eq. (1.52)  summation index "j" 
20  2nd line after (1.52)  ... T with respect to q_{j} (and therefore also with respect to dq_{j}/dt)vanishes. ... 
20  last sentence in paragraph after Eq. (1.52)  ... with respect to the angle coordinate ... 
21  Eqs. (1.54) and (1.55)  both q_{i} should be q_{j} 
21  Eq. (1.47)  after Qj replace "=" with "defined as" symbol. See (1.47) 
22  2^{nd} & 3^{rd} lines after Eq. (1.60)  4 places  change (t,x,y,z) to (x,y,z,t) for normal order 
23  below Eq. (1.64)  ...to the partial time ... 
23  last equation  needs a subscript i to the x on both sides. 
24  first line of Eq. 1.69, after last equality  subscript should be j not i 
24  Eq. (1.69)  all sums are from i =1,n where n is the number of particles in the system 
24  equation on the 2^{nd} line below Eq. (1.69)  "a" should not be bold, "v" should be bold, add a minus sign on the right 
26  three lines below Eq. (1.75)  replace n with thetahat 
26  5_{th} line from the bottom  ... cyclindrical coordinates, restricted to the z = 0 plane, where ... 
27  line just above 2. Atwood's  N^{(e)} = 
27  Figure 1.6  add x to horizontal axis and y to vertical axis. replace n with thetahat, replace r(theta) with r(theta)_{rhat}, etc. 
28  6^{th} line below figure  greek delta should be partial derivative symbol 
29  2^{nd} display equation  first "=" should be "" 
29  5^{th} line above Derivations  r = r_{o}e^{wt }for a bead initally at rest on the wire shows that ... 
29  5^{th} & 4^{th} line above Derivations  ... bead moves exponentially outwards. Again, the ... 
29  2^{th} line above Derivations  L = m r^{2}w = m w r_{o}^{2} e^{2wt}
L, F and N are not bold. 
29  line above Derivations  F = 2 m r_{o} w^{2} e^{wt} 
29  Derivation 2  right hand summation add i not equal to j below the i,j 
31  first equation in Exercise 9  both A's and grad sign should be bold 
31  Exercise 9  Since the text material uses c = 1, remove the c here or add it in the text equations. 
32  6^{th} line  to 2.1 km/s and a mass... 
33  3^{rd} line  Eq.(1.56) 
33  Exercise 20  last term in the equation   V^{2}(x) 
36  Add above Figure  Eq. (2.3) assumes that x is unidirectional between x_{1} and x_{2}. Otherwise the integral must be broken into undirectional subintegrals and the results algebraicly added. 
40  5^{th} line in "2. Minimum..."  Replace x with y and y with x. It is conceptually important to use a variable which is unidirectional over the range of integration. As the following shows, correct results may (but not will) be obtained in some cases even if this principle is ignored. 
41  Figure title  add  Note that this curve is unidirectional in y but not x, so it is best to redo the calculation as described on page 40. 
43  first new paragraph  The parametric solution ... 
43  below last correction (2^{nd} display equation from bottom)  x = a(phisin(phi)), y = a(1cos(phi)) 
43  last equation on page  (y/a)^{3} = (9/2) (x/a)^{2} 
43  Figure 2.4b caption  Cycloid solution to the .... 
45  This section needs to be titled and revised on this page up to the last line as shown  2.4 EXTENSION OF HAMILTON’S PRINCIPLE TO SYSTEMS WITH CONSTRAINTS We discussed in Section 1.3 how problems with holonomic constraints, those that satisfy Eq. (1.37), may be solved by choosing generalized coordinates such that the constraint equations (1.37) become 0 = 0 in this coordinate system. In this section we show that Hamilton’s principle can be extended to solve not only holonomic but, ay t least in a formal sense, to cover …(pick up the last line on page 45) 
46  add at the end of the first full paragraph  In particular, should we set the time integral of the variation of the Lagrangian equal to zero or should we set the variation of the time integral of the Lagrangian equal to zero? These are equivalent for holonomic constraints but give different results for nonholonomic constraints. Studies of the results of these two choices shows that the former is the correct choice. (See footnotes on pg 47) 
46  modify Eq. (2.20) to include time  Replace ") = 0" with "; t) = 0" 
46  line below Eq. (2.20)  …called semiholonomic. If there is no dependence on the velocities these are just the holonomic constrains of Eq. (1.37) 
46  2nd line above Eq. (2.20') to Eq. (20.20')  Equation (2.20) is more general than the commonly used restricted form, linear in d(qa)/dt, f^{a} = (Sum over k)(b_{ak}(q's,t) (d(q_{k})/dt) ) + b_{a}(q's,t) = 0 (2.20') 
46  in first line of last paragraph  …extra virtual displacements for both holonomic and nonholonomic problems is the method 
47
modified 5/24/06 
footnote should readThis is more than the 6^{th} has.  J Ray, Amer J. Phys. 34 (1202),1966; E. J. Saletan & A. H. Comer, Amer J. Phys. 38(892897), 1970. A detailed discussion of nonholonomic constraints is given by M.R. Flannery, "The enigma of nonholomic constraints", Am. J. Phys. 73 (3), March 2005, pp. (265272) 2005 
47  Two lines before Eq. (2.23)  If the constraints are holonomic, we can combine (2.21) with (2.2) giving 
47  following Eq. (2.23)  where the quantity inside the parenthesis can be considered an effective Lagrangian. 
47  2^{nd} through the 4th lines following (2.23)  variables. If the constraints are semiholonomic, the variation must be taken before the integral since we cannot consider the term inside to parenthesis to be an effective Lagrangian. Leaving details to the references*, , the resulting … 
47  revise Eq. (2.25)  Q_{k} = (Sum over b from 1 to m) (lambda_{b} times (partial of f_{b} with respect to the time derivative of q_{k}) 
47  3rd line following (2.25)  … as an n+m nonholomonic system …forces Q_{k}. (delete sentence starting on 3rd line and all of fourth line) 
47  Eq. (2.28)  the 2^{nd} and 3^{rd} terms are replaced by  (lambda)times (time derivative of y) 
47  Eq. (2.29)  the 2nd and 3^{rd} terms are replaced by (lambda) times (time derivative of x) 
47  footnote should read  *J. Ray, Amer. J. Phys. 34 (1202), 1966; E. J. Saletan & A. H. Cromer, Amer. J. Phys. 38 (892897), 1970 
50  third equation from the bottom  no period 
52  5^{th} line, eq. for F_{f}  put "dot" over y 
57  equation after (2.49)  add i below summation 
58  top of page  add i below summation 
59  last summation on page  add i below summation 
65  Exercise 10, 2^{nd} line, grammar change  ... are not known... 
66  Problem 16  s = exp(gamma t/2)q 
68  Exercise 23, 2nd line  ...Let m_{2} be confined to move 
69  add problem (suggested by C Gray  27. (a) Show that the constraint Eq. (2.27) is truly nonholonomic by showing that it can not be integrated to a holonomic form. (b) Show that the corresponding constraint forces are virtu;ary workless (c) Find one or more solutions to (227)(2.30) for V =0 and show that they conserve energy. 
76  2^{nd line }+ minor rewording on lines 10 & 11 to keep page breaks  ...quadratures (evaluating integrals), with ... 
80  Caption for Figure 3.7  This shows the motion of a particle in a central force which is a combination of a 1/r^{3} attractive force and a 1/r^{4} repulsive force. Although there are no stable circular orbits for this set of forces, there are bound, nonclosed orbits, such as the example shown. Thanks to Thomas Fischaleck and Ian Gatland for corrections. 
80  Figure 3.7  This figure should match the cover drawing
Thanks to Thomas Fischaleck and Ian Gatland 
87  Eq. (3.33)  "1" before and inside parentheses should be "l" 
90  above Eq. (3.45)  (from Eq, (3.34) 
90  below Eq. (3.49)  or
r = r_{o} + a cos (beta times theta). 
91  Figure 3.13 As first pointed out by Martin Tiersten Figure 3.13 has been incorrect in the last edition and previous printings of the text.
The caption should read: Orbit for motion deviating slightly from a circular orbit if the central force is given by (beta) = 5. 

95  line below Eq. (3.60)  The coefficient of the linear term in this particular quadratic ... 
98  line above Eq. (3.66)  (3.55) 
99  2^{nd} line  equation reference should be (3.56) 
100  Eq. (3.69)  remove minus sign after = 
100  Eq. (3.72)  put "dot" over theta 
105  fifth line from bottom  subscript of omega is theta 
109  fast form in Eq. (3.99) and in (3.100)  replace e with e^{2} 
109  line above Eq. (3.98)  ... change than writing ... 
110  equation at top of page  replace e with e^{2} 
118  line below Eq. (3.113)  where E = (1/2)m_{1}v_{o}^{2} is the ... 
120  equation below (3.117')  square the cosine term on the right hand side 
121  Fig. 3.37  Replace the x_{i} with r_{i} or modify the caption to s_{i} = x_{j}  x_{k} 
126  Derivation 2, equation  replace sin wt with sin nwt ( w for omega) 
126  last equation in derivation 3  replace sin (...) with sin^{3}(...) and divide rhs by 6 
126  derivation 4  (1...) in deominator is squared 
126  derivation 8  last term on rhs should be "" 
129  Exercise 17, line 2  ...on the orbit 180° out of phase 
129  equation given is for the potentiallhs  V(r) = 
132  exercise 35  reverse the two inequalities 
135  2^{nd} line from bottom  Note that the configuration 
165  display equation above (4.68)  capital omega should be bold face 
166  secondline below (4.71)  capital omega should be bold face 
168  line beloe Eq. (4.77)  ...hence those of V* do not, 
169  Eq. (4.77')  V*_{i} = ... 
174  2^{nd} line above Eqs. (4.87)  axis (omega_{psi}  time derivative of psi). Adding... 
174  Eqs. (4.87)  need "," after each equation 
175  last equation, ratio 366.5/365.5  (366.25/365.25) 
181  Derivation 10, line 3  e^{B} 
181  Derivation 12, 2^{nd} line  replace italic lower case theta with italic lower case phi 
190  Equation above (5.15), after third =  a_{xi} 
191  Section 5.3, first line  L is boldface L 
194  Eq. (5.23)  rho(r)... 
203  footnote  ...which suggests "snakelike." 
206  2^{nd} equationin (5.47)  ... (I_{3}  I_{1}) ... 
209  2^{nd }paragraph, line one  The rates of change... 
209  first of three equations giving the time rates of change  ...= rotation (or spinning) of the top... 
217  above Eq. (5.73)  ...Eqs. (5.71) and ... 
224  last equation on page  factor of 2 Pi missing  but the result is still zero 
224  2^{nd} line  Eq. (5.84) 
231  line above Eq. (5.104)  ... angular velocity for each particle (denoted by i) is 
231  above Eq. (5.105)  (L is a system quantity so summation is taken over repeated i subscripts for the remainder of this chapter) 
231232  Eqs. (5.105), (5.107), (5.110)  replace "+" in front of V with "–" 
240  Eq. (6.8)  first term  drop subscript "i" from "eta" 
241  between Eqs. (6.11) and (6.12)  Change Eq. (6.9) to Eq (6.11)  2 places 
245  6^{th} line below Eq. (6.24)  delta subscripts should be ^{ik} 
245  equation above (6.25)  middle quanity on right hand side should be a_{jl} 
246  4^{th} line above (6.27)  The (no sum on i) clearly applies to the first equation on this line. 
254  3rd of Eqs. (6.55)  omega_{3 } 
256  Eq. (6.58a)  the three matrix elements are a_{11}, a_{21}, and a_{31} 
257  Eq. (6.59)  remember the zeta's and eta's are magnitudes, not unit vectors 
257  Eq. (6.59)  the corrections on p. 256 lead to:
zeta_{1} = (m eta_{1}+M eta_{2} +m eta_{3})/root(2m+M), zeta_{2} = (eta_{1}eta_{3})root(m/2) zeta_{3} = (eta_{1}  2eta_{2} + eta_{3}) x root(mM/(4m+M)). zeta_{1} is center of mass motion 
258  general comments on 3^{rd} paragraph  Angular momentum conservation is not the relevent argument. The motion must be such that all three molecules lie in a plane and the end molecules are always on the same side of the original symmetry axis while the central atom has a smaller displacement to the opposite side. The submitted figure for the 3^{rd} edition was correct but we missed the displacement of the central molecule in proof. This figure may have been corrected in the 4^{th} printing of the 3^{rd} edition. 
266  line above Eq. (6.88)  value ... 
275  Exercise 22  ...V_{11} > V_{22} >0 and... 
276  5^{th} line  implied a preferred inertial frame. ... 
276  7^{th} line  electromagnetic theory without this implication. After... 
276  Eqs. (7.1)  add commas between equations 
276  replace line  F' = (d/dt)P' (7.2) 
279  9^{th} line  ...time interval measured by a clock at rest with respect to that body the proper time of that clock, 
279  4^{th} below Eq. (7.6)  time into three regions,... 
279  right hand side of equation above (7.6)  (1  v^{2}/c^{2}) 
280  first line of Sec. 7.2  ...of transformations between inertial frames that preserve... 
280  second line of Sec 7.2  ...are linear in Minkowski coordinates... 
281  2^{nd} line above Eqs. (7.9)  ...=(ct, r) allows... 
287  2^{nd} line above Eq. (7.30)  two slots (both of which are linear) into which ... 
297  2nd line above (7.66)  the Lorenz condition ... 
298  line below Eq. (7.67b)  holdover from old units. Replace +1/c^{2} with "" and 1/c with 1. Also replace e with q for generality 
298  Eqs. (7.71), (7.71') and (7.71")  multiply lhs by c or divide each element on rhs by c. 
314  Eq. (7.140)  starting with the 2nd "=+ sign =T + mc^{2} + V = E 
320  Eq. (7.159)  leading term on rhs x'^{o}/c ... 
322  Eq. (7.165)  2nd term on rhs, (q/c) 
323  Eq. (7.166) after first inequality  change u superscript to (nu) and multiply expression by g^{(mu)(nu)} 
324  9^{thline of Section 7.11}  ...(paths of extremal distance)... 
328  sign of lambda  There are several notational approaches to GR. Our choice makes k a negative number, hence a negative lambda causes expansion. 
329  Derivations 12  ...are said to form a group (see Appendix B) if ... 
331  Exercise 21  symbol associated with h should be an italic greek nu. Font makes it hard to tell. 
332  Exercises 29 & 30  insert ^{TM }where appropriate 
334  3^{rd} line below Eq. (8.1)  ... or the n q_{i}'s ... 
337  Eq. (8.16)  add dt to the last term on the rhs 
340  add above Eq. (8.25)  gives us, since T is symmetric 
347  8^{th} line below the figure title  ... where cm denotes ... 
351  display equation below (8.56)  superscript should be italic greek nu. Font makes it hard to tell. 
353  Eq. (8.61), righthandside of both equalities  replace superscript in the demoninator by (sigma) and multiply each righthandside by g^{(nu)(sigma)} 
353  Equation above (8.62), after "=" sign  replace superscript (0) with (mu) and multiply expression by g^{0(mu)} 
362  Derivation 3, last line, first p dot  should be a (q dot)_{i} 
364  #14, 5th term on rhs  (ydot)^{2} 
365  last display equation  needs a 2 in the denominator 
367  1^{st} display for Exercise 34, 2^{nd }term  both lamba and nu are equal subscripts 
379  Eq. (9.39b)  the p in the square root should be P 
381  1^{st} line  ... use of canonical transformations ... 
382  Eq. (9.52)  zeta is bold face 
384  2^{nd} line below last display equation  J is bold face and Sans Serif 
386  last line  1 is bold Sans Serif 
388  Eq. (9.70)  subscript eta is bold face 
388  rhs of Eq. (9.69)  [p_{j},p^{k}]_{q,p} 
389  11^{th} line from bottom  eta is bold 
392  Eq. (9.78a)  A and B are bold face 
392  Eq. (9.78b)  A and B are bold face and Sans Serif 
394  footnote  Carathedory has ' over the e 
416  line above Eq, (9.142)  A is bold face and Sans Serif 
423  Derivations 13., first line  ...transformations forms a group (Appendix B). ... 
425  last eqn on page  ...=qB 
428  line above the equation in 36. (b)  ...find a general expression for 
434  line above Eq. (10.14)  principal function ... 
436  Eq. (10.27)  add "." at end 
438  Eqs. (10.35), (10.36), (10.38)  add "," between equations where appropriate 
438  line above Eq. (10.38)  ... The principal function ... 
439  Eqs. (10.35') and (10.42)  add spearating "," as needed 
441  1^{st} of Eqs. (10.46)  Q_{1} = t + (beta)_{1} ... 
446  last paragraph, 1^{st} line  ... a coordinate q_{j} is separable if ... 
446  third line above Eq. (10.56')  "S" should be "s" 
448  line below Eq. (10.63)  Staeckel 
457  3^{rd} line below Eq. (10.99)  interchange p and q 
458  2^{nd} line below Eq. (10.100)  p... in the (q_{i}, p_{i}) plane ... 
460  Line below (10.108)  The differential operator ... 
461  Eq. (10.111)  add an "i" in exponent 
464  9^{th} line  a solution of the HamiltonJacobi equation. 
465  line above Eq. (10.122)  written (where j_{ki} are positive or negative integers) 
471  1^{st} of Eqs. (10.144)  add "," a end 
481  Exercise 25  Show, by the method... 
488  1^{st} of Eqs. (11.9)  add "," after equation 
506  Eqs. (11.29)  add "," after each equation 
509  line below Eq. (11.31)  ... with the variable x restricted to ... 
511  4^{th} line in table caption  replace "=" with "" 
511  3^{rd} line from bottom  produce seemingly random ... 
514  3^{rd} line from bottom  ... and that are considerably ... 
523  Exercises 6 (b) and display for 8  add "." at end of lines 
525  Exercise 16, 2^{nd} line  ... , such as those 
538  line below Eq. (12.51)  ...gravitational radius of the Sun 
543  first of Eqs. (12.69) and Eq.(12.75a)  add "," at end 
543  Eqs. (12.71b) and (12.71c)  symbol following = is a bold face, greek nu 
544  Eq. (12.71d)  symbol following = is a bold face, greek nu 
548  14^{th} line  of (J_{o}' ... 
550  Eq. (12.96)  add a bar above the lhs to show this is an average and replace the bar over the a on the left hand side with two dots to show a second derivative 
553  Eq. (12.107)  lower case greek omega is not bold face 
555  Exercise 2, 1^{st} line  ... vertically hung Hooke'slaw ... 
556  Exercise 6. (b)  Use firstorder perturbation ... 
556  Exercise 7, below display equation  ... constant. Use firstorder timeindependent ... 
558  2^{nd} line  ... afinite, or at ... infinite, number ... 
564  Eq. (13.18)  place a "," before the x on the rhs. Note that the comma in the middle tewrm is a subscript as it should be. 
567  Eq. (13.32), denominator of 2^{nd} term on right  dx^{j} 
583  line below Eq. (13.94)  move and from in front of two equations to between the two equations 
593  last eqn on page  ...+O(a(dot), a(double dot)) 
594  2^{nd} below Eq. (13.142)  ... helpful, however, to ... 
596  6^{th} line below Eq. (13.154)  ... for the (spinless) KleinGordon ... 
601  2^{nd} line above Eqs. (A.1y)  ... Temporarily using ... 
606  5^{th} and 6^{th} lines below Table B.1  DELETE "We shall use h for the group order." 
608  2^{nd} line above Eq. (B.10) and 2^{nd} line below Eq. (B.11)  add a "," in each 
611  following 6^{th} line below Table B.4 Add caption  TABLE B.5 Characteristics of the Dihedral Group D_{3} 
611  3^{rd} line before LIE GROUPS AND ALGEBRAS  ... = 0. In quantum... 
612  line following Eq. (B.16)  ... c_{ij}^{k} =  c_{ji}^{k}) ... 
612  Eq. (B.18)  first k is a subscript to the summation  i.e. sum over k 
616  first line  TEXTBOOKS 
624  entry for Lagrange, J. L.  14, 123, 198, ... 
625  Apsidal >> vector  page 87 not 86 
626  Boost  Boost, 282, ... 
626  Coriolis >> effect  125 not 126 
629  Force .. centrifugal  175, 176 
631  Inertial >> force, 5  Inertial >> frame, 2 
632  Lorentz >> boost  282 not 284 
635  Quadrature  75, 76, 211 
636  Scattering >> laboratory coordinates,  114120 
cover

Comment on the cover figure  The cover figure shows the motion of a particle around a central force source. There are two central forces acting; an attractive force proportional to 1/r^{3} and a repulsive force proportional to 1/r^{4}. The figure was probably inspired by the hard core repulsive nuclear force. 
xi

add paragraph  additional akowledgements and a reference to this site 
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