Question

Show that the system of differential equations is Hamiltonian, and find a Hamiltonian function H(x,y). You may assume that H(0,0) = 0. 3y2 - 2.c dx dt dy dt 6x2 + 2y

Please show all work if possible, thanks!

Answer 1

an - 3 1 - - 2 0 dt = 6*2 23 dt To show diff" ear is Hamiltonian da at xt K = ( K'x) { Ketxy = (Ru) at Hamiltonian Now To show system to flay)= ah Не — he не - = (x) е ХО Те — 2н 27 28 tе op - - к с С he се he ?н дух Chirot _ з 2-х fe - 2 9 к с — 2 / sinace fe he се – he て一こ ке 80 system is Hamlltonian

эн chirst he - 2 x не he 깷 32-2 ня, у ) = 3- 2 y + a(x) where acu) ist of a - 25 та — не ке 22 Fee - 6x* -- ( Вку в - — re - 2 + 4 - - 6х-23 re да Әя - - 62 а (х) = - 2х3 — 23 - 2 ху chiro H