→ adu :謝謝幫忙:) 06/28 03:54
※ 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
^^^^
...主詞是什麼?
: system at the origin with domain R^2.
x' = [(r - r^3)/2]cosθ - rsinθ
= x - y - (x^2 + y^2)x/2
y' = [(r - r^3)/2]sinθ + rcosθ
= y + x - (x^2 + y^2)y/2
(x_0, y_0) = 0
linearize
x' = (1 - (3/2)(x_0)^2)x + (-1 - (y_0)(x_0))y
y' = (1 - x_0y_0)x + (1 - (3/2)(y_0)^2)y
x' = x - y
y' = x + y
不知道是不是再問這個?
這個方程式是可以直接解的
r = r(θ)
dr/dθ = (r - r^3)/2
=> r/√(1 - r^2) = Cexp(θ/2)
θ = t + θ_0
: 2.Show that:
: x' = x+y^2
: y' = -y
: and
: x'=x
: y'=-y+4x^3
: are Hamiltonian.
你問問題前應該先定義說明Hamiltonian的意思
有很多名詞是用Hamiltonian當名稱
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