14復暯柺嬋慄丒嬻娫嬋慄

丂丂丂暯柺嬋慄丂P(t)丂=丂(丂sint,丂cost),丂t∈[0,2兾]丂傪昞帵偡傞偵偼丄師偺傛偆偵擖椡偟傑偡丅

亜丂plot(丂[丂sin(t)丂,丂cos(t)丂,丂t=0丂.丂.丂2丂*丂Pi丂]丂)丂

丂丂丂傑偨嬋慄偑昞帵偝傟傞椞堟偺廲偲墶偺斾傪摨偠偵偡傞偵偼丄師偺傛偆偵擖椡偟傑偡丅

亜丂plot(丂[丂sin(t)丂,丂cos(t)丂,丂t=0丂.丂.丂2丂*丂Pi丂]丂,丂scaling=constrained丂)丂

丂丂丂師偵丄嬻娫嬋慄丂P(t)丂=丂(丂t,丂t²,丂t³丂)丂,丂t∈[-1,1]丂傪昞帵偡傞偵偼丄

亜丂with(plots):丂
亜丂spacecurve丂(丂[丂t丂,丂t^2丂,丂t^3丂],丂t=-1丂.丂.丂1丂)丂

偲擖椡偟傑偡丅夋柺忋僪儔僢僌偡傞偙偲偵傛傝丄嬻娫嬋慄傪條乆側妏搙偐傜尒傞偙偲偑偱偒傑偡丅嬋慄偼僨僼僅儖僩偱200屄偺揰偐傜惗惉偝傟傑偡偑丄嬋慄傪傛傝妸傜偐偵昞帵偡傞偵偼丄

亜spacecurve丂(丂[丂t丂,丂t^2丂,丂t^3丂],丂t=-1丂.丂.丂1丂,丂numpoints=n丂)丂丂

(n偼廫暘戝偒側帺慠悢丂)偲擖椡偟傑偡丅
丂丂丂偦傟偱偼埲壓偺幚廗丂14.1丂乣丂14.6丂偺嬋慄傪昞帵偟偰傒傑偟傚偆丅

幚廗丂14.1丂丂寽悅慄丂P(t)丂=丂(丂t,丂(e^t+e^-t)丂/丂2丂),丂t∈[-1,1]

幚廗丂14.2丂丂儕儅僜儞丂P(t)丂=丂(丂(cost+a)丂cost,丂(cost+a)丂sint丂),丂t∈[0,2兾]
(1)丂a = 1.5 偺偲偒丂丂丂丂 (2)丂a = 1.0 偺偲偒丂丂丂丂(3)丂a = 0.5 偺偲偒

幚廗丂14.3丂丂P(t)丂=丂(丂tant,丂1丂/丂cost丂),丂t∈[-兾/6,兾/6]

幚廗丂14.4丂丂傾僗僥儘僀僪丂P(t)丂=丂(丂cos³t,丂sin³t丂),丂t∈[0,2兾]

幚廗丂14.5丂丂P(t)丂=丂(丂e^tcost,丂e^tsint丂),丂t∈[0,30]

幚廗丂14.6丂
(1) P(t)丂=丂(丂cost,丂sint,丂t丂),丂t∈[0,6兾]
(2) P(t)丂=丂(丂tcost,丂tsint,丂t丂),丂t∈[0,6兾]

暯柺嬋慄丂儭:丂P(t)丂=丂(丂x(t)丂,丂y(t)丂),丂t∈[a,b]丂偺挿偝偼

嬻娫嬋慄丂儭: P(t)丂=丂(丂x(t)丂,丂y(t)丂,丂z(t)丂),丂t∈[a,b]丂偺挿偝偼

(偄偢傟傕丄∫^b_a丂||P'(t)||丂dt偺宍)丂偱梌偊傜傟傑偡丅偙偺岞幃傪梡偄偰嬋慄偺挿偝傪寁嶼偟偰傒傑偟傚偆丅旝暘丒愊暘偵偮偄偰偼丂10復傪嶲峫偵偟傑偟傚偆丅

幚廗丂14.7丂慜偺幚廗丂14.4丂乣丂14.6丂偺嬋慄偺挿偝傪媮傔偰傒傑偟傚偆丅昁梫偑偁傟偽丄

亜丂simplify丂(幃)丂

偲偟偰娙扨側宍偱抣傪媮傔偰傒傑偟傚偆丅

14復 暯柺嬋慄丒嬻娫嬋慄