The key difference from Lagrangian mechanics is that the Hamiltonian approach groups variables into pairs of coordinates called the phase space coordinates:This leads to having two times more unknown functions than in the Lagrangian. However, it also leads to a system of partial differential equations with only first order derivatives, which is nicer. Notably, it can be more clearly seen in phase space.
- generalized coordinates, generally positions or angles
- their corresponding conjugate momenta, generally velocities, or angular velocities
There is a Turing machine that halts for every member of the language with the answer yes, but does not necessarily halt for non-members.
Video "Finite fields made easy by Randell Heyman (2015)" at youtu.be/z9bTzjy4SCg?t=159 shows how for order . Basically, for order , we take:For a worked out example, see: GF(4).
- each element is a polynomial in , , the polynomial ring over the finite field with degree smaller than . We've just seen how to construct for prime above, so we're good there.
- addition works element-wise modulo on
- multiplication is done modulo an irreducible polynomial of order
This is how you transform the Lagrangian into the Hamiltonian.
Xavier Niel, Iliad - Free: Je suis un casseur de monopoles by DECIDEURSTV (2011)
Source. Title translation: "I'm a hunter of monopolies". Unlisted articles are being shown, click here to show only listed articles.