22復 旝暘曽掱幃(楢棫曽掱幃)

1. 曻暔塣摦
悈暯曽岦偵偼慜復偺戞1愡偱妛傫偩摍懍塣摦丄悅捈曽岦偵偼摍壛懍搙塣摦傪偡傞摦揰偺摦偒傪峫偊偰傒傑偟傚偆丅
椺偊偽丄x 幉曽岦偵堦掕偺懍搙2丄y 幉曽岦偵堦掕偺壛懍搙 -9.8 偱摦偔摦揰 P 偺帪崗 t 偵偍偗傞埵抲傪 (x(t),y(t)) 偲昞偡偲

x'(t)= 2丄丂y''(t)= -9.8

偑惉傝棫偪傑偡丅弶婜忦審 x(0)=0, y(0)=0, y'(0)=9 傪枮偨偡夝傪媮傔丄僔儈儏儗乕僔儑儞傪峴偭偰傒傑偟傚偆丅

>with(DEtools):

>dsolve({diff(x(t), t) = 2, diff(y(t), t, t) = -9.8, x(0) = 0, y(0) = 0, (D(y))(0) = 9}, {x(t), y(t)})

>plot([rhs(op(1, %)), rhs(op(2, %)), t = 0 .. 2], scaling = constrained)

>animate(pointplot, [[rhs(op(1, `%%`)), rhs(op(2, `%%`))]], t = 0 .. 2, scaling = constrained, symbol = solidcircle, symbolsize = 40)

>display({%, %%})

偲擖椡偟昤偐傟偨僌儔僼傪僋儕僢僋偟偰昞帵偝傟傞儊僯儏乕僶乕忋偺傾僯儊乕僔儑儞嵞惗儃僞儞傪 僋儕僢僋偡傞偲丄傾僯儊乕僔儑儞偑巒傑傝傑偡丅



2. 惗懺宯(儘僩僇丒儃儖僥儔曽掱幃)
偁傞俀庬椶偺惗暔庬X,Y偺帪崗t偵偍偗傞屄懱悢偑偦傟偧傟x(t),y(t)偲昞偣丄x偲y偺曄壔偑師偺旝暘曽掱幃(宯)偵廬偆偲偟傑偟傚偆丅



偙偙偱丄a1偲a2偼偦傟偧傟X偲Y偺庬撪偺憹怋棪丄b1偲c2偼庬撪偺嫞憟棪傪堄枴偡傞偲偟傑偡丅 傑偨丄c2偲b1偼庬娫憡屳嶌梡偐傜掕傑傞掕悢偲偟傑偡丅c1偲b2偑偲傕偵惓偺抣偺偲偒曽掱幃偼嫤挷宯偲傛偽傟丄偲傕偵晧偺偲偒嫞憟宯丄c1偑惓偱b2偑晧偺偲偒曔怘幰丒旐怘幰宯偲傛偽傟傑偡丅椺偊偽丄a1=a2=b2=c1=1, b1=c2=0偺偲偒丄偡側傢偪丄

x'=x(1+y),丂y'=y(1+x)


偺夝嬋慄傪丂xy 暯柺忋偵恾帵偟偰丄惗懺宯偺帪娫曄壔傪挷傋偰傒傑偟傚偆丅

>with(DEtools):

>de1:=[diff(x(t),t)=x(t)*(1+y(t)),diff(y(t),t)=y(t)*(1+x(t))]

>ini1:=seq([x(0)=0.2*i,y(0)=0.9-0.2*i],i=1..4)

>DEplot(de1,[x(t),y(t)],t=0..30,[ini1],x=0..4,y=0..4,stepsize=0.1)


幚廗22.1
儘僩僇丒儃儖僥儔曽掱幃宯偵偍偄偰丄師偺応崌偵夝嬋慄傪恾帵偟側偝偄丅
(1)a1=a2=b1=c1=c2=1
(2)a1=a2=b2=c1=1,b1=c2=-1
(3)a1=a2=1,b1=b2=c1=c2=-1
(4)a1=a2=b1=b2=c2=-1,c1=1
(5)a1=b2=1,b1=c2=0,a2=c1=-1

[惓夝椺]



3. 擬懳棳 (儘乕儗儞僣曽掱幃)
忋壓偺暯峴側暻偺娫偺塼懱偵懳偟丄壓偺暻偺壏搙偑忋偺暻偺壏搙傛傝廫暘戝偒偄偲偒偵婲偙傞懳棳塣摦偼儘乕儗儞僣曽掱幃



偵傛傝婰弎偝傟傑偡丄偙偙偱丄冃=10, r=28, b=8/3 偺偲偒丄僇僆僗尰徾偑娤嶡偝傟傞偙偲偑抦傜傟偰偄傑偡丅Maple傪梡偄偰丄偙偺偲偒偺弶婜忦審x(0)=y(0)=z(0)=10傪枮偨偡曽掱幃偺夝偺対摦傪挷傋偰 傒傑偟傚偆丅

>de2:=[diff(x(t),t)=-10*(x(t)-y(t)),diff(y(t),t)=-x(t)*z(t)+28*x(t)-y(t),diff(z(t),t)=x(t)*y(t)-8/3*z(t)]

>DEplot3d(de2,{x(t),y(t),z(t)},t=0..50,[[x(0)=10,y(0)=10,z=(0)=10]], scene=[x(t),y(t),z(t)],x=-50..50,y=-50..50,z=0..50,stepsize=0.01)


拲堄 夝偼晄婯懃偵怳晳偆偙偲偑抦傜傟偰偄傑偡丅傑偨丄夝偺嬌尷廤崌偼儘乕儗儞僣傾僩儔僋僞乕偲傛偽傟偰偄傑偡丅


幚廗22.2丂弶婜忦審傪曄偊偰儘乕儗儞僣曽掱幃偺夝傪媮傔恾帵偣傛丅

[惓夝椺]