This page contains all known corrections and suggestions to the 6^{th} 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/r^{3} attractive and a 1/r^{4} repulsive force. or another possibility is an 1/r^{2} attractive and a 1/r^{3} 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  2^{nd} 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  
159/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 xyaxis, v would need to be parallel to the xaxis. A proper perspective drawing with y parallel to v would be better.  
16  3^{rd} 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 Q_{j} 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  2^{nd} line above Eq. (1.57') ***is an appropriate Lagrangian ...***  
23  Eq. (1.67)  the x, y, and z in k_{x}, k_{y}, and k_{z} should all have the subscript i .  
24  Eq. (1.68)  add the subscript i to the grad_{v}  
24  5 Oct 07  Eq, (169)  since the sum is over all i, add the subscript i to the grad_{v }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 ... ***  
27Aug 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 r_{o} cosh(wt) and even a sum of cosh and sinh, replacing the expontial term in the angular momentum by cosh^{2}(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 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..."***  
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. ***  
4647  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. 2^{nd} 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. (265272) 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 x_{1} = x_{2}, y_{2} = y_{1} > 0. Express the condition for the parameter a as a transcendental equation in terms of the dimensionless quantities k = x_{2}/a and <beta> = y_{2}/x_{2}. Show that there is a value <beta>_{0} for which only one value of k is possible, a range of values of <beta> for which there are two solutions for k and ranges of <beta> and k for which no solutions exist; so no catenary solution exists for those ranges. Find the value of <beta>_{0}, numerically if necessary.  
67 4/22/10 
The exponent of e should be : 2(Gamma)t/2  
68  22/8/06  Exercise 21  2^{nd} line ***...force constant K whose***  
69  19/8/06  Exercise 26  1^{st} 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 onebody 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  8^{th} text line  the first greek theta should match the symbol on the 4^{th} line  
118Aug 07  line following Eq. (3.112)***Unless there are excited internal degrees of freedom in the socalled Q ***  
120  10^{th} line from the bottom ***...momentum is conserved (and ***  
120122  both figures are drawn with ellipses having the same eccentricity.  
124  9/Sept/06  6^{th} line above figure ***...local potential extremum*** 4^{th} 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: e^{3} sin^{3} ((omega)t... 

126 29/9/06  Derivation 4, equation at the bottom of the page. Remove the ^{2} from the (1V/E) and add it to the last term ***...s^{2}(1rho^{2})^{2}***  
127 9/4/09  Derivation 6 ***drops off monotonically***  
129  1/11/06  Exercise 19b, 2^{nd} line, *** by pi([rho]/a)^{2} per revolution,...***  
1299/4/09  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  3^{rd} 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 I_{1} with I_{2}  
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  3^{rd} line following figure caption ***...only when f(u) is positive...***  
221  4^{th} line following the figure caption ***the third root u_{3} is then less than ***  
225  22/8/06  2^{nd} line after 3^{rd} 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  5^{th} 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  4^{th} line after Eq. (6.26') *** coordinates ***  
250  22/8/06  4^{th} 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  7^{th} line in last full paragraph ***...molecule is classically meaningless...***  
268  last line of title for Fig. 6.7: ***...case omega_{c} <<...***  
269  Inside Figure 6.8 the i subscript (omega_{i}) should be (omega_{o})  
271  8^{th} 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  S_{1} 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  4^{th} line following Eq. (7.34') remove ")" following coordinates.  
293  9^{th} 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  3^{rd} line from bottom Note that the E contains mc^{2} 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 a_{y}  
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. (824a) & (824b) Middle terms use [ ] around the row matrix.  
34121/8/07  Eq. (8.28'), next to last term. space is needed after the sin^{2}theta.  
34121/8/07  3^{rd} line from bottom should read L = T  U =...  
34221/8/07  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  4^{th} line after last equation ***advantage. It is ...***  
360  22/8/06  Eq. (7.32') ***(ds)^{2} = ...***  
361  22/8/06  2^{nd} line  ***...(cf. Eq. (7.32'))***  
364  11/Apr/08  Exercise 16 Equation *** H = p^{2}/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 P_{i} 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 

3779/4/09  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. 91(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  3^{rd} line, 2^{nd} 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  6^{th} line from bottom the J should be J  
392  line following Eq. (9.77):***generally noncommutive...***  
393  Eq. (981) there should be a "," between all the p and q subscripts.  
395  22/8/06  Eq. (9.89) Second equation F^{1}(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 Apr08  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  2^{nd} line from top, 2^{nd} equation P_{2} = 2q_{1}  q_{2}
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 F_{2} the q_{i} should be q_{1}  
434 4/21/10  Last term in equation 10.14 should read *** (alpha) t ***  
436  5^{th} line above Eq. (10.30):***...Hamilton's principal function...***  
438  2^{nd} 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) *** H_{j}(... ***  
451  21/8/07  Eq. (10.74'), numerator of the 2^{nd} term on the lhs. The subscropt should be phi
3rd line after equation (10.77) ***Equation (10.76) says the zcomponent of the *** 

459 22/8/06  5^{th} 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  2^{nd} 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  3^{rd} line after Eq. (10.121) ***...If only m of the n***  
465  After the Sum symbol ***j_{ki} w_{i}  
467  22/8/06  3^{rd} 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  3^{rd} line of Exercise 5 ***...of the HamiltonianJacobi 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 P_{1} should be P_{i}  
499  22/8/06  3^{rd} line above Eq. (11.25): there should be a plus/minus sign in front of 0.408  
505  22/8/06  6^{th} line in Section 11.7 ***...set of 2N firstorder...***  
514  22/8/06  In Eqs. (11.39 ) through (11.41b), all subscipt n should be italic. Also in the 3^{th} through 6^{th} 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 4^{th} power  
531  Eqs. (12.21)  first equation, last term omega is raised to the 5^{th} power  
532  footnote  delete 5th word.  
533  22/8/06  End of second line  there should b a dot over c_{i} to indicate derivative Also in the equation following the second set of brackets shloud be "[...]" not "{...}"  
534  3^{rd} equation on the page, 3^{rd }term  ***...)^{4} ...***  
537  extend bar over entire left hand side term  
542  Eq. (12.64) 3^{rd} term on rhs is epsilon^{2}  
542  line below Eq. (12.66)  replace a by lower case Greek alpha  
543  Eqs, (12.71b) and (12.71c)  the bold v_{o }should a bold ( Greek) nu_{o}  
545 22/8/06  9th line above Eq. (12.80) ***the 19^{th} 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  7^{th} line ***T_{i} with components T_{ij }***  
571  22/8/06  3^{rd} 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  3^{rd} 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& 
Eq. (A.11xyz): Lower left matrix element, second term, replace sin <theta> with sin <phi> 

APPENDIX B  
606  Middle display Eq. (B.1) *** i^{3} = i ***  
608  First line after Eq. B11: ***whose only solution is l_{1}_{ = }l_{2 }= 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 2^{nd} Ed.  
619  First reference on Chapter 11  author's name should read ***Hao BaiLin*** as per the edition referenced. Chinese name order also appears as Bailin Hao and Hao Bailin  
AUTHOR INDEX  
624  Lorenz, E.N., 523 Lorentz, H. A. 577 

632  Lagrange multipliers, 16, 46, 67 

637  delete page 339 from reference "Symplectic,approach" 
If I have left on a name, please notify me. Page maintained by John Safko
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