4. A Hamiltonian system in R2 is a system of the formандуx'-(x, y)Hy'-(x, y)where H: R² → R is a C function called the Hamiltonian function.?x(Ideal Pendulum.) The system of equations0' =vv=sin 0describes the motion of an undamped pendulum.(a) Show that this system is a Hamiltonian system (i.e. find a Hamiltonian function for thissystem).(b) Determine all the critical points of the system.(c) Plot several trajectories of the system. Indicate the direction of the motion on each tra-jectory. (Hint: use part (a).)

(a) The system is given by θ'=νν'=-sinθ. So now, according to the description of a Hamiltonian…

Answered: 4. A Hamiltonian system in R2 is a…

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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