Да в первом томе ещё даже неголомные связи есть, параграф 38
в связи с этим хочется привести одну выдержку
[A.M. Bloch: Nonholonomic mechanics and control. Springer]:
"Variational Nonholonomic Equations. It is interesting to compare
the dynamic nonholonomic equations, that is, the Lagrange–d’Alembert
equations with the corresponding variational nonholonomic equations. The
distinction between these two different systems of equations has a long and
distinguished history going back to the review article of Korteweg [1899]
and is discussed in a more modern context in Arnold, Kozlov, and Neishtadt
[1988]. (For Kozlov’s work on vakonomic systems see, e.g., Kozlov [1983]
and Kozlov [1992]).8 The upshot of the distinction is that the Lagrange–
d’Alembert equations are the correct mechanical dynamical equations,
while the corresponding variational problem is asking a different question,
namely one of optimal control.
Perhaps it is surprising, at least at first, that these two procedures give
different equations. What, exactly, is the difference in the two procedures?
The distinction is one of whether the constraints are imposed before or
after taking variations. These two operations do not, in general, commute."
.
, иначе при отрицательной скорости она весело будет разгонять тело.