This page contains all known corrections and suggestions to the 6th and later printings.

It is interesting that although contributions have been made by many, there has been almost zero overlap of their corrections and suggestions. This page will be updated periodically as new suggestions are received.

.The corrections are usually set off by *** ***, any comments on the corrections follow

These first entries were posted in early May 2005 Any additions since then have the page numbers in boldand, usually also have the date the correction was posted.

Last revision was made 4 April 2010

 page# Correction Cover The cover picture shows the motion of a particle under central forces. There is a 1/r3 attractive and a 1/r4 repulsive force. or another possibility is an 1/r2 attractive and a 1/r3 repulsive force. As discussed in Section 3.6 the orbit does not close. Special thanks to Thomas Fischaleck and Ian Gatland for pointing this out to us. CHAPTER 1 4 - 7/Sept/06 2nd line ***...friction is always negative and*** 5 last line *** ...forces, if they obey ... 6 First full sentence following Eq. 1.23 *** of mass, (1.22), can be restated*** 8 First line:***Equations (1.22 and (1.26)*** 14 Tltle for Figure 1.4 *** Double plane pendulum 15-9/Apr 09 It has been pointed out that Fig. 1.5 has had a geometric inconsistency since the 1st Edition. To agree with the viewpoint of the xy-axis, v would need to be parallel to the x-axis. A proper perspective drawing with y parallel to v would be better. 16 3rd line from bottom *** ... consistant with the constraints ...*** (virtual displacements need not be consistant with the forces) 20 In the first display expression above Eq. (1.52) delete the -Qj term. This only an expansion of the preceding expression below (1.51) 20 2nd line below Eq(1.52) -- no correction needed 20 end of paragraph below (1.52) It is understood that T makes sense only in an inertial system. 21 2nd line above Eq. (1.57') ***is an appropriate Lagrangian ...*** 23 Eq. (1.67) -- the x, y, and z in kx, ky, and kz should all have the subscript i . 24 Eq. (1.68) -- add the subscript i to the gradv 24 - 5 Oct 07 Eq, (169) -- since the sum is over all i, add the subscript i to the gradv in all places and to all sum signs 24 ling below Eq. (1.69) don't start a new paragraph and change line ending to *** ... moving at a velocity v, *** (vector not scalar) 24 line above Eq. (1.70) --- start a new paragraph 26 line following Eq. (1.75) ***.of Eq. (1.75), without suppressing z, is obtained ... *** 27-Aug 07 Fig. 1.6 caption replace r by r 27 line below figure *** make Greek theta bold face *** it is a vector 29 last text section above the Derivations *** the solution is made more general by replacing exp(wt) with ro cosh(wt) and even a sum of cosh and sinh, replacing the expontial term in the angular momentum by cosh2(wt) + ... and in the force F replace exp(wt) with sinh(wt), (In the preceeding w is the lower case Greek omega).*** 31 - 10 Apr 08 First equation in Exercise 9 -- t should not be bold 31 19/10/06 Derivation 9: Remove the 1/c in the phi transformation. Wrong units for eqns. on pg. 22 32 25/6/09 Exercise 20 -- Equation --rhs, 2nd term should be – not + CHAPTER 2 36 add above Figure ***Eq. (2.3) assumes that x is unidirectional between x1 and x2. Otherwise the integral must be broken into undirectional sub-integrals and the results algebraicly added. 40 5th line in "2. *** Minimum..."*** 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. *** 46-47 Eqs. 2.20, 2.21, 2.23, 2.26- and 2.27 all summation subscripts should be greek/symbol alpha as should the subscript if a in eq. 2.25. line following Eq. 2.23: The subscripts of both Q should be the same. 2nd line following Eq. 2.25 for clarity ***...are possibly functions of all the...*** 47 All lower case mass "m" should be "M". In line 3 of the second paragraph, x/r = sin(theta), this makes z = -r cos(theta), this changes a sign in cos(theta) term of the second Lagrange equation. In the second of the display equations in this paragraph, the right hand side should be divided by a. 47 replace footnote ***J. Ray, Amer. J. Phys. 34 (1202), 1966; A detailed discussion of nonholonomic constraints is given by M.R. Flannery, "The enigma of nonholomic constraints", Amer. J. Phys. 73 (3), March 2005, pp. (265-272) 2005*** 48 first line should read ***...(2.26). These two sets (Eq. (2.25)*** 48 - 5 Oct 07 line below Eq. 230c ***((2.29 and (2.30))*** 49 First line of paragraph containing Eq. (2.35) and line following that equation:add equation (2.24) so it reads ***Eqs. (2.20) or (2.24) *** 50 11/Apr/08 add to Eq. 2.36 *** -lambda(r (Theta)dot - x*dot) *** 54 26/6/09 Equation at top of page -- rhs, last term -- replace e by E 63 - 7/Sept/06 Equation above (2.59) -- insert minus (-) sign on right hand side 65 - 23/Mar/07 Exerise 7:Change text to***In Example 2 of Section 2.2, we considered the problem of the minimum surface of revolution. Examine the symmetric case x1 = x2, y2 = -y1 > 0. Express the condition for the parameter a as a transcendental equation in terms of the dimension-less quantities k = x2/a and = y2/x2. Show that there is a value 0 for which only one value of k is possible, a range of values of for which there are two solutions for k and ranges of and k for which no solutions exist; so no catenary solution exists for those ranges. Find the value of 0, numerically if necessary. 67 4/22/10 The exponent of e should be : 2(Gamma)t/2 68 - 22/8/06 Exercise 21 - 2nd line ***...force constant K whose*** 69 - 19/8/06 Exercise 26 - 1st line ***...by a massless string of length...*** CHAPTER 3 73 line following Eq. (3.8) *** ... From (3.7) it also *** 76 First line, Sec. 3.3: ***solved the equivalent one-body problem*** 92 2nd line, first full paragraph:***still give closed orbits?*** 104 Fig. 3.18 The vectors titled mk should be multiplied by a unit vector in the r direction 115 - 22/8/06 8th text line -- the first greek theta should match the symbol on the 4th line 118-Aug 07 line following Eq. (3.112)***Unless there are excited internal degrees of freedom in the so-called Q *** 120 10th line from the bottom ***...momentum is conserved (and *** 120-122 both figures are drawn with ellipses having the same eccentricity. 124 - 9/Sept/06 6th line above figure ***...local potential extremum*** 4th line above figure ***energy is a maximum only...*** 4th line above figure ***...axis, and increases in directions*** 126 - 22/8/06 Derivation 1, line below equation ***provided the motion...*** 126 - 4/24/10 Derivation 3. First Equation needs a minus sign on the right hand side and in the last fullequation last equation, rhs, the first sine is cubed: e3 sin3 ((omega)t... 126 -29/9/06 Derivation 4, equation at the bottom of the page. Remove the 2 from the (1-V/E) and add it to the last term ***...s2(1-rho2)2*** 127 9/4/09 Derivation 6 ***drops off monotonically*** 129 - 1/11/06 Exercise 19b, 2nd line, *** by pi([rho]/a)2 per revolution,...*** 129-9/4/09 1st line-- *** Yukawa *** 130 - 1/11/06 Exercise 21: change Show that ... to Consider... Add a period after the next equation and delete the two lines following lines. First line after the second equation change to ***...precess (after the correction of 5600" for known...*** 131 Exercise 28a: Delete the "c" from 2nd term, right hand side. CHAPTER 4 137 - 22/8/06 Eq. (4.2) -- delete the 2nd column in the set of equations -- also on line following Eq. (4.3) ***,,,nine direction cosines...*** 136 delete first two words below the title for Fig. 4.2. (a repeat from preceeding page) 137 Eqs. (4.2) -- Delete last equals and contents for all equations. 160 mod 8/4/09 Eq. (4.31) Show the ***summation over the subscript i in the second equation*** 168 - 22/8/06 The S in the first unmumbered equation should not be bold. 170 - 22/8/06 Caption for Figure 4.12 the x', y', and z' should not be bold 171 - 22/8/06 End of section 4.9 -- move the period to after the ")". 173 - 22/8/06 3rd line -- the epslon should not be bold. 176 Eq. at bottom of page add ***s-1 ***corrects units 181 - 7/22/07 Problem 13 - second sentence should read***Show that Phi1/2, Phi2/2 and Phi/2 can be considered*** All angles should be divided by 2. This is the half angle formula. CHAPTER 5 184 - 22/8/06 8th line ***between the change of states...*** 194 - 22/8/07 & 9/4/09 Last sentence on page ***...tensor possess a type of symmetry relative to the center...*** 197 - 22/8/07 second line above Eq. (5.35) ***desiginated as the inertia ellipsoid.***[tensor not tenson] 200 Sec. 5.6, third line ***at rest or moving uniformly*** 206 24/6/09 2nd line in Eqn.(5.47) ,both sides (2 places) replace I1 with I2 209 - 22/8/07 Last symbol in the first complete pargaraph on page... This symbol should be the same l used in Fig, 5.7. That is ***point will be denoted by l.*** 214 3rd line following figure caption ***...only when f(u) is positive...*** 221 4th line following the figure caption ***the third root u3 is then less than *** 225 - 22/8/06 2nd line after 3rd unnumbered equation. The I should be bold not italic. 233 - 29/9/08 revised 5/25/07 Derivation 5 starting with Eqs. (5.39) are replaced by (there are two terms in the rotating frame) Do not sum on "i" in the first equation but sum over "j" and "k". So the first equation is three equations one each for i = 1, 2, 3.. CHAPTER 6 243 - 22/8/06 line after Eq. (6.20) -- reference should be to Eq. (6.20) 244 - 22/8/06 5th line after Eq. (6.23 ***Eqs. (6.12) and (6.22a)...*** 245 Eq. (6.26') the V in this equation is the transformed diagonal V 245 4th line after Eq. (6.26') *** coordinates *** 250 - 22/8/06 4th line after Eq. (6.35) The second subscript should be a lower case k. 252 immediately above Eq. (6.47) ***Equations (6.46)...*** 257 - 22/8/06 7th line in last full paragraph ***...molecule is classically meaningless...*** 268 last line of title for Fig. 6.7: ***...case omegac <<...*** 269 Inside Figure 6.8 the i subscript (omegai) should be (omegao) 271 8th line from the bottom. Equation reference should be (6.92) not (6.93) CHAPTER 7 281 4/22/10 Equation on line before Eq.(7.10): r and r' should be italic r and r' 283 Eq. (7.16) -- replace ( ...) with [ ...] -- this is a matrix 284 24/6/09 Second text line above Eqn. (7.19) replace Since with since 284 - 22/8/06 next to last line Eq. 4.43 also -- S1 should not be bold 285 - 22/8/06 line below Eq. (7.24) ***... is frequently*** 288 - 22/8/06 In Eq. (7.32') ***(ds)2 = ...*** 291 - 22/6/06 4th line following Eq. (7.34') remove ")" following coordinates. 293 9th line from bottom *** (E/c, p) is a ...*** E should not be bold 311 - 22/8/06 3rd line above Eq. (7.129) ***inition of Eq.(7.128) the reference...*** 316 line before Eq. (7.146)***velocity in the x direction as 316 3rd line from bottom-- Note that the E contains mc2 as shown at the top of page 317 317 Eq. (7.150) inside "[" *** [1+ ...*** 317 - 22/8/06 line below Eq. (7.15) ***The integral in ...*** 317 Eq. below (7.150) inside "(" *** (1+...*** 317 Eq. (7.151) replace "3" by "-3" 327 - 22/8/06 last full paragraph -- delete the last word (existing) 329- 21/8/07 Derivation 7, center equation of the three in this problem. The numerator should be ay 332 24/6/09 Second line in Exercise 29- replace (7.17) with (7.18) 332 - 22/8/06 last line -- ***...the Schwarzschild so-*** CHAPTER 8 334 last line on page: Delete the words ***problem in n inde-*** A repair for the repeat in the top line on 335. 339 Eqs. (8-24a) & (8-24b) Middle terms use [ ] around the row matrix. 341-21/8/07 Eq. (8.28'), next to last term. space is needed after the sin2theta. 341-21/8/07 3rd line from bottom should read L = T - U =... 342-21/8/07 second paragraph:*** Because of this linear term in U, the Hamiltonian is not T + U. However, it is still in this case the total energy, T + V since the"potential "energy...**** 349 - 22/6/06 4th line after last equation ***advantage. It is ...*** 360 - 22/8/06 Eq. (7.32') ***(ds)2 = ...*** 361 - 22/8/06 2nd line -- ***...(cf. Eq. (7.32'))*** 364 - 11/Apr/08 Exercise 16 Equation *** H = p2/2a ...*** 265 24/6/09 Eqn. in part )b) – no minus sign 366 - 22/8/06 3rd line from bottom ***...of the particles with ...*** CHAPTER 9 373 29/8/06 line below Eq. (9.16) the Pi at the end of the line should have a "dot" over it. 276 29/9/06 Equation above (9.30) interchange the off disgonal elements Equation below (9.30) interchange the two off diagonal elements 377-9/4/09 Eq. (9.32a): The subscript on F should be 1. 378 - 22/8/06 footnote: 3rd line from bottom: the alpha should be a lower case omega. 380 Fig. 9-1(d) Label the vertical axis *** P *** capital letter 384 24/6/09 Near the middle of the page 3,3 element in Matrix M should be -1 389 last unnumbered display Eq. on page: replace the u in the first partial with v. 391 3rd line, 2nd display equation. The partial derivative in the numerator should be of second order. 391 line following Eq. (9.77):***...the derivative with respect to...*** 391 - 22/6/06 6th line from bottom the J should be J 392 line following Eq. (9.77):***generally noncommutive...*** 393 Eq. (9-81) there should be a "," between all the p and q subscripts. 395 - 22/8/06 Eq. (9.89) Second equation F1(q, Q) 397 line above Eq. (9.96) ***Eq. (9.67) we have *** 397 line following Eq. (9.96) *** ...way of writing Eq. (8.39). ...*** 401 replace the "," after U(q,p) with a "." 402 line following Eq. (9.106):***...equation of motion Eq. (9.94),...*** 404 Eq. (9.114) ***(r x p)*** vectors 411 - -11 Apr-08 First eqation --- p should be bold & italic 415 - 22/8/06 Eq. (9.137) the A should be A 417 - 22/8/06 line below Eq. (9.147) *** By straightforward manipulation...*** 422 - 21/8/07 in problem 7(b) *** F3 type for the identity transformation*** and *** F4 type for the exchange transformation*** 423 -22/08/06 21/8/07 2nd line from top, 2nd equation P2 = -2q1 - q2 First line of problem 12 ***for a canonical transformation are given*** 425 24/6/09 equation should read qB/m in SI units or qM/mc in Gaussian units 426 - 11/Apr/08 Exercise 27a -- equation *** ... = (1/2)(xi)T S (xi) *** 429 25/6/09 Exercise 41 – an example of the constant epslon could be a charge q CHAPTER 10 431 Eq. (10.3)first of the terms involving the partials of F2 the qi should be q1 434 4/21/10 Last term in equation 10.14 should read *** (alpha) t *** 436 5th line above Eq. (10.30):***...Hamilton's principal function...*** 438 2nd line from bottom-- replace F by W 439 second of Eqs. (10.41) -- replace 2 inside square root by 4 444 line above Eq. (10.49)***are separable. In this case a solution...*** 444 Eq. (10.50) *** Hj(... *** 451 - 21/8/07 Eq. (10.74'), numerator of the 2nd term on the lhs. The subscropt should be phi 3rd line after equation (10.77) ***Equation (10.76) says the z-component of the *** 459 -22/8/06 5th line after Eq. (10.106) ***...variables imply that ...*** 460 - 22/8/06 In Eq. (10.110') the second a in the right hand side should be e 461 - 22/8/06 2nd line above Eq. (10.115) ***separable variable pairs...*** 463 - 22/8/06 Eq. (10.119) the limit is taken as T goes to the limit 464 - 22/8/06 3rd line after Eq. (10.121) ***...If only m of the n*** 465 After the Sum symbol ***jki wi 467 - 22/8/06 3rd line from bottom replace "integral over" by "integral of theta" 478 25/6/09 Derivation #4: all the terms of the form J/Pi should have a square root on them. 478 3rd line of Exercise 5 ***...of the Hamiltonian-Jacobi equation for...*** 480 25/6/09 Last line Exercise 16 should ;;;less than or equal to Pi/2 482 25/6/09 Delete the primes (') on all the J's. CHAPTER 11 484 Insert Above 11.1**We have skipped the field of complexity which is the range of problems which are not chaotic, but are too complex for reliable predictions using the methods developed in the preceding and following chapters. 488 - 22/8/06 first of Eqs. (11.10) - the P1 should be Pi 499 - 22/8/06 3rd line above Eq. (11.25): there should be a plus/minus sign in front of 0.408 505 - 22/8/06 6th line in Section 11.7 ***...set of 2N first-order...*** 514 - 22/8/06 In Eqs. (11.39 ) through (11.41b), all subscipt n should be italic. Also in the 3th through 6th lines following Eq. (11.41b) CHAPTER 12 528 Eq. (12.5) --- replace the subscript "i" on the rhs by a subscript "1" 530 Eqs. (12.20) -- first equation, last term --omega is raised to the 4th power 531 Eqs. (12.21) -- first equation, last term --omega is raised to the 5th power 532 footnote -- delete 5th word. 533 - 22/8/06 End of second line -- there should b a dot over ci to indicate derivative Also in the equation following the second set of brackets shloud be "[...]" not "{...}" 534 3rd equation on the page, 3rd term -- ***...)4 ...*** 537 extend bar over entire left hand side term 542 Eq. (12.64) 3rd term on rhs is epsilon2 542 line below Eq. (12.66) -- replace a by lower case Greek alpha 543 Eqs, (12.71b) and (12.71c) -- the bold vo should a bold ( Greek) nuo 545 22/8/06 9th line above Eq. (12.80) ***the 19th century...*** 546 Equation below (12.28b) replace H by J CHAPTER 13 562 26/6/09 right hand side of (13.14) replace a with greek alpha 563 - 22/8/06 last symbol on page should be an italic greek symbol mu. 567 - 30/11/06 Eq. (13.28) - lhs - 2nd term -- raise the greek nu 571 - 30/11/06 7th line ***-Ti with components -Tij *** 571 - 22/8/06 3rd line above Eq. (13.44) ***...vector, we expect...*** 573 - 30/11/06 following Eq (13.54) to the end of the page - Pi index must be superscript and eta index must be subscript. 578 - 30/11/06 3rd line DELETE (and therefore H) and at the end of the line ***should be a scalar*** 584 - 30/11/06 Eq. 13.101 - rhs -add a comma before the greek nu in the second term 594 - 22/8/06 Eq. (13.145) second term on the right hand side: the denominator should have the partial derivative symbol. 600 26/6/09 Last integral -- upper limit should be x not infinity. APPENDIX A 603 - 23/Mar/07& 9 Apr/09 Eq. (A.11xyz): Lower left matrix element, second term, replace sin with sin Also the (1,1) term should be -cos cos APPENDIX B 606 Middle display Eq. (B.1) *** i3 = -i *** 608 First line after Eq. B11: ***whose only solution is l1 = l2 = 1*** 611 Renumber Table B.5 to B.4 and Table B.4 to B5. On line above what was originally B.5 add*** See table B.4*** 5th line below second table (was B.5 now B.4) ***In Table B.5 the ...*** SUGGESTED BIBLIOGRAPHY 617 Reference to Hestenes should include 2nd Ed. 619 First reference on Chapter 11 -- author's name should read ***Hao Bai-Lin*** as per the edition referenced. Chinese name order also appears as Bailin Hao and Hao Bailin AUTHOR INDEX 624 Lorenz, E.N., 523Lorentz, H. A. 577 632 Lagrange multipliers, 16, 46, 67 637 delete page 339 from reference "Symplectic,approach"
Contributors to the above (in alphabetical order) are
Ravinder Arbol; Brent Barker; Michael Baer; Loshua Beun; Carol Braun; Turan Birol; Alonso Botero; Peter M. Brown; Dometris Charalambous; Jose' David Cojal; Frank Dick; Joseph Eimer; Mike Ellis; Dave Freund; Thomas Fischaleck; Davide Fiocco; M. R. Flannery; Samuel Friedman; Ian Gatland; Adam Gretchell; K, F. Gauss, Qiang LI; John L. Jones; Gerald Kasner; Yevgeny Kats; Charles Korn; Neeraj Kumar; Luca Labardi; Velimir Labinac; Joshua Lande; Marc Y H Landeweer; Eric Lawrence; Olli Lehtonen; Peifeng Liu; Drew Milsom; Michael Nauenburg; Dave Nero, Mathew Orr; Brett Palmer, Daniel Phillips; Nachum Plonko; Andrew Pontzen; Harold Salwen; Min Schrader; Steven Schwarz; Chris Stevens; Andy Tenne-Sens; Julius T Su; Dick Tripping(!); Ronald Webber; Brett Williams, Yang Withers; Joao Carlos Xavier; Alex Joseph Yuffa

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