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Tagged with hamiltonian-mechanics sg.symplectic-geometry
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Substitution of the old variable to a generating function
Assume that we have one of the 4 types of generating functions (say F(p, Q)) which defines a symplectomorphism $T$:
$(P,Q) = (u(p,q), v(p,q))$. Now we can make a substitution and get a function $G(p,q)...
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On the measure of regular and chaotic regions in a phase space
Consider a Hamiltonian, non-linear, dynamical system associated to $H(\vec{q},\vec{p})$. Assume that the number of effective degrees of freedom is relatively small, say $D=3,4,5$. Now choose a certain ...
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