Re: Newton Vs Lagrange Vs Hamilton

Frank Hellmann wrote: 
Yes. One can convert any Hamiltonian system into a Lagrangian system
in extended phase space. But one can convert a Lagrangian system into
a Hamiltonian one only if d^2L/dq^2 is nonsingular.


That is only correct if you ignore the possibility to work with
constraints. Without constraints you can't even handle simple
relativistic systems though, so this is usually assumed to be part of
the Hamiltonian method. See the appendix of gr-qc/0110034 or Diracs
Lecture on QM (Here you'll find the original ideas that allowed GR to
be cast into Hamiltonian form).

True. But one would usually refer to this as a 'constrained Hamiltonian system' and not just as a 'Hamiltonian system'.

Constrained Hamiltonian systems and Lagrnaigian systems are almost
equivalent. One still needs a constant rank assumtpion to go from
a Lagraingian to a Hamiltonian.


Arnold Neumaier



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