Consider the following two-dimensional dynamical system,p(x, y) Hдуdxdtdy) - (PladtƏHOxIt is clear that if p(x,y)=1 everywhere, this system is Hamiltonian by definition.where p(x,y) a "smooth enough" function.-p(x, y)-1- What general property must the function p(x,y) satisfy for this system to beHamiltonian?-2- Using the property of p(x,y) you derived in -1-, find the largest family of p(x,y) (i.e.the most general function) that guarantees the system is still Hamiltonian.-3-Show that, for an arbitrary and nice enough p(x,y), H(x,y) is a conserved quantityfor this system.

Answered: Image /qna-images/answer/e258e175-7b05-4c86-adba-8474f3981198.jpg

Answered: -1- What general property must the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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