長さの違う複数の振子を同じ初期角から一斉に振る。
各糸の長さは、たとえば同じ 30 秒間に振子 1 は 15 往復、振子 2 は 16 往復、振子 3 は 17 往復 ...... するように設定する。
参考:
Pendulum Waves
Pend = class() function Pend:init(funcs, t0, inits, h, numOfDiv, len, radius, color) self.len = len self.radius = radius self.color = color self.Unpack = unpack or table.unpack self.Sin = math.sin self.Cos = math.cos self.funcs = funcs self.t0 = t0 self.inits = inits self.dim = #funcs self.numOfDiv = numOfDiv or 1 self.h = h / self.numOfDiv self.f = {{}, {}, {}, {}} self.temp = {{}, {}, {}} end function Pend:updateRK() for i = 1, self.numOfDiv do for j = 1, self.dim do self.f[1][j] = self.funcs[j](self.t0 , self.Unpack(self.inits)) ; self.temp[1][j] = self.inits[j] + self.h/2 * self.f[1][j] end for j = 1, self.dim do self.f[2][j] = self.funcs[j](self.t0 + self.h/2, self.Unpack(self.temp[1])) ; self.temp[2][j] = self.inits[j] + self.h/2 * self.f[2][j] end for j = 1, self.dim do self.f[3][j] = self.funcs[j](self.t0 + self.h/2, self.Unpack(self.temp[2])) ; self.temp[3][j] = self.inits[j] + self.h * self.f[3][j] end for j = 1, self.dim do self.f[4][j] = self.funcs[j](self.t0 + self.h , self.Unpack(self.temp[3])) end for j = 1, self.dim do self.inits[j] = self.inits[j] + self.h/6 * (self.f[1][j] + 2 * (self.f[2][j] + self.f[3][j]) + self.f[4][j]) end self.t0 = self.t0 + self.h end return self end function Pend:print() print(self.t0, "{"..table.concat(self.inits, ", ").."}") return self end function Pend:drawTime(gc, x, y, fontSize) local x, y = x or 10, y or 10 local fontSize = fontSize or 10 gc:setFont("sansserif", "r", fontSize) gc:drawString(string.format("t = %.1f", self.t0), x, y) return self end function Pend:drawPend(gc, cx, cy, unit) local lenOnScr = unit * self.len local radiusOnScr = unit * self.radius local diaOnScr = 2 * radiusOnScr local sx = cx + lenOnScr * self.Sin(self.inits[1]) local sy = cy + lenOnScr * self.Cos(self.inits[1]) gc:setColorRGB(self.color) gc:drawArc(sx - radiusOnScr, sy - radiusOnScr, diaOnScr, diaOnScr, 0, 360) gc:drawLine(cx, cy, sx, sy) return self end --- 確かめる。 do platform.window:setBackgroundColor(0x000000) local isTicking = false local W, H, CX, CY, UNIT, FONT_SIZE function on.resize() W, H = platform.window:width(), platform.window:height() CX, CY = W/2, H/40 UNIT = H/1.05 FONT_SIZE = H/16 end local colors = {0xc6c6ff,0xc1c1ff,0xbcbcff,0xb7b7ff,0xb2b2ff,0xa8a8ff,0xa8a8ff,0xa3a3ff,0x9e9eff,0x9999ff,0x9393ff,0x8e8eff,0x8989ff,0x8484ff,0x7f7fff} local lens = {0.96285212588934,0.84625676136746,0.74945046484677,0.66851360342403,0.60015560057340,0.54160430424661,0.49120194251045,0.44751739096444,0.40962625507320,0.37611413577122,0.34662680356814,0.32056136826120,0.29711721061937,0.27636562941545,0.25760882741459} local radiuses = {0.05,0.045,0.041,0.036,0.032,0.030,0.027,0.024,0.022,0.020,0.017,0.016,0.014,0.013,0.011} -- この聯立微分方程式を解く。 local function radDot(t, rad, vel, len) return vel end local function velDot(t, rad, vel, len) return -(9.80665/len) * math.sin(rad) - 0.01 * vel end -- 0.01 * vel は諸々の減衰項。 local function lenDot(t, rad, vel, len) return 0 end -- 長さの違う複数の振子をインスタンス化する。 local pends = {} local function reset() for i = 1, #lens do pends[i] = Pend({radDot, velDot, lenDot}, 0, {0.5, 0, lens[i]}, 1/64, _, lens[i], radiuses[i], colors[i]) -- (函数リスト, t0, {初期角度，初期角速度}, 刻み幅 [, 内部分割数], 糸の長さ, 分銅の半径, 色) end end function on.construction() reset() end function on.enterKey() if isTicking == false then timer.start(pends[1].h) ; isTicking = true elseif isTicking == true then timer.stop() ; isTicking = false end end function on.escapeKey() reset() end function on.timer() for i = 1, #lens do pends[i]:updateRK() -- タイマーの tick するたびにインスタンスを更新する。 end platform.window:invalidate() end function on.paint(gc) gc:setColorRGB(colors[1]) pends[1]:drawTime(gc, 10, 0, FONT_SIZE) for i = #lens, 1, -1 do -- 奥の振子から順番に描く。 pends[i]:drawPend(gc, CX, CY, UNIT) end end end
