On p.27, the first sentence of section 1.5.1
is missing a "the"
--------------------------------
On p.72, there is an "Arnoldian" error.
Though the text states that the state-advancer advances to a
stated final time, that argument is actually the time increment.
But the example starts from 0 so you cannot tell whether that
argument is a delta-t or a final-t.
--------------------------------
On p.84, in equation 1.150
the factor Dt (DF~(s))(t, x')
should have a v' in the argument list
Dt (DF~(s))(t, x', v')
--------------------------------
On page 110, in exercise 1.39 part d
English grammar error: delete the words "differences of the".
----------------------------------
On page 176, in exercise 2.18
equations 2.144 and 2.144
The second 144 should probably be a 145 (unless there
is a mathematical joke behind the repetition).
----------------------------------
In the exercise about symplectic integration many "2pi"'s ought to be
replaced by "1/2pi".
----------------------------------
In equation 2.96 the middle entry in the bottom row of the 3x3 matrix
should have a minus sign.
----------------------------------
Page 141, first paragraph, first sentence:
The two occurrences of the word "if" are incorrect. The clause
following each is a parenthetical.
Because of our ordering A <= B <= C the longest axis of this triaxial
energy ellipsoid coincides with the \hat{c} direction (All of the
angular momentum is along the axis of largest principal moment of
intertia.) and the shortest axis of the ellipsoid coincides with the
\hat{a} axis (All of the angular momentum is along the axis of
smallest principal moment of intertia.).
----------------------------------
Page 145, Figure 2.4
The angle phi should be measured from the -y axis not the x axis. The
sequence of rotations for our Euler angles, from the reference
position with the axis of the top vertical, are
psi around the z axis
theta around the x axis
phi around the z axis
The result of the rotation by theta around the x axis tilts the top
from the z axis to the -y axis. The next rotation then displaces the
top in longitude away from the -y axis. Sorry.
----------------------------------
Page 175, Last paragraph.
Delete the irrelevant (and incorrect) sentence:
"In fact, the are the only algebraically closed field besides
complex numbers."
----------------------------------
Equations 1.185 and 1.186 are a bit funny.
Lambda compose Gamma[q] = lambda
but in these equations Lambda has been replaced by lambda
even though there is still a composition with Gamma[q].
----------------------------------
There is a hidden (non explicit) use of commutation in the action
derivation of Hamilton's equations.
----------------------------------
Equation 5.92 on p. 348 has an error. The L_e^\prime on the second
line should just be L_e.
----------------------------------
There is an extra "that" in the sentence just after equation 5.98 on
p. 349.
----------------------------------
on p. 274 (paraphrased):
Consider the system
Dz(t) = F(t, z(t))
or
Dz^i(t) = F^i(t, z^1(t), ... , z^n(t))
for i=1 to n
where n is the dimension of the state space.
If F depends on t then the "state" is not just z^1(t) to z^n(t), but
must also include t. n is the dimension of z, not the dimension of
the state.
Also, why is this 1-based instead of 0-based as the rest of the book?
----------------------------------
on p. 278 I is called the "identity function" by it is really a
multiplicative identity. (It is not a function of anything. Of
course it will be different depending on what it multiplies.)
----------------------------------
In the sentence just before equation 4.27 on p. 278, the word
"show" should be "shows".
On p.279, last paragraph, there is a missing "a". The sentence should
read: "If the reference trajectory is a fixed point ..."
----------------------------------
This is not an error in the book, but it is a proof by assertion. On
page 204 (Properties of the Poisson bracket) we blithely assert that
{F, G} = - {G, F} -- not admitting that this is hairy if F and G have
structured arguments. Thus the conservation of the Hamiltonian is
also not obvious by this argument. The commutation of the partial
derivatives depends on the commutability of tuples that are compatable
for contraction.
----------------------------------
On p.340 the sentence before 5.68 says "Abstracted to functions of
phase-space states ..." but there is nothing to abstract. It is the
same as eq 5.67. Apparently, 5.67 was improved, but the followup
sentence leading to 5.68 was not adjusted.
On p.348 eq.5.92 second line... the "L'_e" should be just "L_e"
----------------------------------
In the sentence just before eq.5.99 there are two "that"s. There
should just be one.
We should think about whether "q_t" aught to be replaced by "t"
everywhere in the extended phase space section. The advantage of
"q_t" is that it is evidently one of the coordinates. But it is
confusing to have two different names for the same thing.
----------------------------------
Well, the "E" in eq.5.124 is funny. Isn't E the value of the
Hamiltonian along solution paths, not the value of H on an arbitrary
state.
----------------------------------
P.244 Code does not work as written because of lack of (null)
parameters for state-advancer.
The code as printed is:
(define (HHmap E)
(let ((advancer
(state-advancer
(phase-space-derivative HHHam))))
(lambda (y py cont fail)
(define (find-next-crossing s)
(let lp ((s s))
(let ((ns (advancer s .1 1.e-12)))
(if (and (> (ref (coordinate ns) 0) 0)
(< (ref (coordinate s) 0) 0))
(refine-crossing s)
(lp ns)))))
(define (refine-crossing s)
(let ((dt (- (/ (ref (coordinate s) 0)
(ref (momentum s) 0)))))
(let ((ns (advancer s dt 1.e-12)))
(if (< (abs (ref (coordinate s) 0))
1.e-10)
;; return new section point
(cont (ref (coordinate ns) 1)
(ref (momentum ns) 1))
;; continue refining
(refine-crossing ns)))))
(let ((initial-state (section->state E y py)))
(if (not initial-state)
(fail)
(find-next-crossing initial-state))))))
It should have been
(define (HHsysder)
(phase-space-derivative HHHam))
(define (HHmap E)
(let ((advancer (state-advancer HHsysder)))
(lambda (y py cont fail)
(define (find-next-crossing s)
(let lp ((s s))
(let ((ns (advancer s .1 1.e-12)))
(if (and (> (ref (coordinate ns) 0) 0)
(< (ref (coordinate s) 0) 0))
(refine-crossing s)
(lp ns)))))
(define (refine-crossing s)
(let ((dt (- (/ (ref (coordinate s) 0)
(ref (momentum s) 0)))))
(let ((ns (advancer s dt 1.e-12)))
(if (< (abs (ref (coordinate s) 0))
1.e-10)
;; return new section point
(cont (ref (coordinate ns) 1)
(ref (momentum ns) 1))
;; continue refining
(refine-crossing ns)))))
(let ((initial-state (section->state E y py)))
(if (not initial-state)
(fail)
(find-next-crossing initial-state))))))
----------------------------------
On page 451, the second term on the right hand side of equation 6.29
should have a minus sign. Similarly, on page 453, the right hand side
of equation 6.32 should be negated.
--------------------------------