Re: [微分方程] 線性化跟Hamiltonian

[jumbajuice (jumba)]

※ 引述《adu (^_^)》之銘言：
: 1.Consider the system in polar coordinates
: r' = (r-r^3)/2
: theta' = 1
: Show that on the unit disk D = {r < 1} is conjugate to the linearised
: system at the origin with domain R^2.

: 2.Show that:
: x' = x+y^2
: y' = -y
取 H(x,y)= x*y+ (y^3)/3 +c

如此一來 x'= dH/dy, y'= -dH/dx   這裡 "d" 是偏微分的意思

依照下面網頁上equation (2) 的定義, 這是一個Hamiltonian system
http://www.scholarpedia.org/article/Hamiltonian_systems

: and
: x'=x
: y'=-y+4x^3
: are Hamiltonian.

取 H(x,y)=..

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→ adu         :謝謝:)