# 일반수학및실습2-11.7절

## 2465 days 전, jhlee2chn 작성

예.

var('a, t') assume(a>0) f(t)=a*cos(t);g(t)=a*sin(t) r(t)=[f(t), g(t)] v=diff(r(t), t) vn=v.norm().simplify_full() print "||v(t)||=", vn
 ||v(t)||= sqrt(a^2*abs(cos(t))^2 + a^2*abs(sin(t))^2) ||v(t)||= sqrt(a^2*abs(cos(t))^2 + a^2*abs(sin(t))^2)
T=v/vn cur=diff(T, t).norm()/vn show(cur)
 \newcommand{\Bold}[1]{\mathbf{#1}}\frac{\sqrt{{\left| -\frac{a \cos\left(t\right)}{\sqrt{a^{2} {\left| \cos\left(t\right) \right|}^{2} + a^{2} {\left| \sin\left(t\right) \right|}^{2}}} \right|}^{2} + {\left| -\frac{a \sin\left(t\right)}{\sqrt{a^{2} {\left| \cos\left(t\right) \right|}^{2} + a^{2} {\left| \sin\left(t\right) \right|}^{2}}} \right|}^{2}}}{\sqrt{a^{2} {\left| \cos\left(t\right) \right|}^{2} + a^{2} {\left| \sin\left(t\right) \right|}^{2}}}

예.

var('t') f(t)=2*sin(t);g(t)=2*cos(t);h(t)=3*t r(t)=[f(t), g(t), h(t)] parametric_plot3d(r(t), (t, 0, 4*pi))
 Sleeping...
dr=diff(r(t), t);d2r=diff(dr, t) drn=dr.norm() num=dr.cross_product(d2r).norm() den=drn^3 k=num/den print k
 sqrt(abs(-4*cos(t)^2 - 4*sin(t)^2)^2 + abs(6*cos(t))^2 + abs(-6*sin(t))^2)/(abs(2*cos(t))^2 + abs(-2*sin(t))^2 + 9)^(3/2) sqrt(abs(-4*cos(t)^2 - 4*sin(t)^2)^2 + abs(6*cos(t))^2 + abs(-6*sin(t))^2)/(abs(2*cos(t))^2 + abs(-2*sin(t))^2 + 9)^(3/2)

예.

t=var('t') r=vector((cos(t), sin(t), t)) T=diff(r, t)/norm(diff(r, t)) N=diff(T, t)/norm(diff(T, t)) B=T.cross_product(N) p1=parametric_plot(r, (t, -pi, pi), color='goldenrod', thickness=2) p2=sum([arrow3d(r(t=x), r(t=x)+T(t=x), width=1) + arrow3d(r(t=x), r(t=x)+N(t=x), color='red', width=1) + arrow3d(r(t=x), r(t=x)+B(t=x), color='green', width=1) + point3d((cos(x), sin(x), x), pointsize=20) for x in [-3..3,step=1]]) show(p1+p2)
 Sleeping...