5 votes
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Is this hamiltonian of the form of some well-known physical system?

One likely candidate for what they "want you to say" is a Kepler potential (i.e. produced by an inverse distance-squared force) viewed in a rotating frame that scales the rotation rate by a ...
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4 votes

What is the correct general form of Hamilton's equation?

Most generally the observable $F$ depends not only on $q(t)$ and $p(t)$, but also depends on $t$ explicitly, i.e. $$F=F(q,p,t)$$ Differentiating this with respect to time $t$ you get $$\begin{align} \...
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2 votes
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Would it be more insightful to teach students Lagrangian/Hamiltonian mechanics before Newtonian mechanics?

The concept of energy comes with luggage. Potential energy does not have an intrinsic zero point. If you have two position coordinates then what is definable is the potential difference between the ...
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1 vote
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Finding a new hamiltonian from a given canonical transformation

Since you know the new $q(Q)$, it’s easier to use another generating function $F(p,Q)=pq(Q)$ (Legendre transform of your function) which gives: $$ q = \frac{\partial F}{\partial p}(=q) \\ P = \frac{\...
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  • 1,182
1 vote
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Can a primary constraint contain spatial derivative of the field?

Yes, in field theory the primary constraints can contain spatial$^1$ derivatives of the canonical fields. One example is when Legendre transforming the Nambu-Goto (NG) string action, see e.g. this ...
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  • 167k
1 vote

Spin Orbit Coupling Hamiltonians

No, these are not always the same thing. Spin-orbit coupling in atoms Spin-orbit coupling can be derived by reduction of the Dirac equation to non-relativistic limit, as one of several relativistic ...
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