f(t)=t^t的拉普拉斯变换是什么，怎么求解？ f(t)=t^t的拉普拉斯变换是什么，怎么求解？
f(t)=t^t\u7684\u62c9\u666e\u62c9\u65af\u53d8\u6362\u662f\u4ec0\u4e48\uff0c\u600e\u4e48\u6c42\u89e3\uff1f\u7528\u79ef\u5206\u5b9a\u7406\uff1a\u82e5f\uff08t\uff09=\u79ef\u5206g\uff08t\uff09dt\uff0c\u5219F(s)=G(s)/s+f\uff080-\uff09/s \u9636\u8dc3\u54cd\u5e94\u4e3a1/s\uff0c\u539f\u51fd\u6570\u4e3a1 \u5bf9\u9636\u8dc3\u54cd\u5e94\u7684\u539f\u51fd\u6570\u79ef\u5206\uff0c\u5f97t\u7684\u8c61\u51fd\u6570\u4e3a1/s^2 \u5bf9t\u79ef\u5206\uff0c\u5f97t^2/2\u7684\u8c61\u51fd\u6570\u4e3a1/s^3 \u5219t^2\u7684\u8c61\u51fd\u6570\u4e3a2/s^3 \u4e0d\u61c2\u8ffd\u95ee
\u7528\u79ef\u5206\u5b9a\u7406\uff1a\u82e5f\uff08t\uff09=\u79ef\u5206g\uff08t\uff09dt\uff0c\u5219F(s)=G(s)/s+f\uff080-\uff09/s
\u9636\u8dc3\u54cd\u5e94\u4e3a1/s\uff0c\u539f\u51fd\u6570\u4e3a1
\u5bf9\u9636\u8dc3\u54cd\u5e94\u7684\u539f\u51fd\u6570\u79ef\u5206\uff0c\u5f97t\u7684\u8c61\u51fd\u6570\u4e3a1/s^2
\u5bf9t\u79ef\u5206\uff0c\u5f97t^2/2\u7684\u8c61\u51fd\u6570\u4e3a1/s^3
\u5219t^2\u7684\u8c61\u51fd\u6570\u4e3a2/s^3
\u4e0d\u61c2\u8ffd\u95ee
绛旓細鎷夋櫘鎷夋柉閫鍙樻崲鏄凡鐭(s) 姹傝В f(t) 鐨勮繃绋嬨傜敤绗﹀彿 琛ㄧず銆傛媺鏅媺鏂嗗彉鎹鍙樻崲鐨勫叕寮忔槸锛氬浜庢墍鏈夌殑t>0锛f(t)= mathcal ^ left =frac int_ ^ F(s)' e'ds锛宑' 鏄敹鏁涘尯闂寸殑妯潗鏍囧硷紝鏄竴涓疄甯告暟涓斿ぇ浜庢墍鏈塅(s)' 鐨勪釜鍒偣鐨勫疄閮ㄥ笺
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绛旓細鈭玙0^鈭濬(s)= f(t)e^{-st}dt 鎷夋皬鍙樻崲鍦ㄥぇ閮ㄤ唤鐨勫簲鐢ㄤ腑閮芥槸瀵瑰皠鐨勶紝鏈甯歌鐨 f(t) 鍜 F(s) 缁勫悎甯稿嵃鍒舵垚琛紝鏂逛究鏌ラ槄銆傛媺姘忓彉鎹㈠拰鍌呯珛鍙跺彉鎹㈡湁鍏筹紝涓嶈繃鍌呯珛鍙跺彉鎹㈠皢涓涓嚱鏁版垨鏄俊鍙疯〃绀轰负璁稿寮︽尝鐨勫彔鍔狅紝灞炰簬銆岄鍩熷彉鎹嶏紱鑰屾媺姘忓彉鎹㈠垯鏄皢涓涓嚱鏁拌〃绀轰负璁稿鐭╃殑鍙犲姞锛屽睘浜庛...
绛旓細姝ｇ‘銆傛瘮濡傚嚱鏁f(t)=t 鍙婂垎娈靛畾涔夊嚱鏁帮細 f(t)= t锛 (t鈮2)锛 10,(t=2)杩欎袱涓嚱鏁鐨勬媺鏅媺鏂彉鎹閮戒负L{f(t)}=1/s^2 浣嗗畠浠槸涓嶅悓鐨勪袱涓嚱鏁般
