Cinem\303\241tica Curvilinea: Usando Componentes Vectorialesphysicsleninac@hotmail.comJSFHJSFH<Text-field style="Heading 1" layout="Heading 1">Instrucciones</Text-field>- Primero realice la siguiente acci\303\263n:Cargar las librerias a utilizar: use DocumentTools in
restart:with(VectorCalculus):
end use;
JSFH- Rellene los campos el indica; ingresar el vector posici\303\263n- Finalmente click en los botones respectivosJSFHJSFH<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Componentes de la Aceleraci\303\263n</Font></Text-field>
Espacio\342\210\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 los vectores posici\303\263n:r[t] = mLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYxLUkjbWlHRiQ2KVEoU3R1ZGVudEYnLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRicvJSVib2xkR1EmZmFsc2VGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJStleGVjdXRhYmxlR0Y0LyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNjFRIltGJ0YvRjJGOEY7L0Y+USdub3JtYWxGJy8lJmZlbmNlR0Y3LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjcvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMTY2NjY2N2VtRicvJSdyc3BhY2VHRlYtRiw2KVEvVmVjdG9yQ2FsY3VsdXNGJ0YvRjJGNUY4RjtGPS1GQTYxUSJdRidGL0YyRjhGO0ZERkZGSEZKRkxGTkZQRlJGVC9GWFEsMC4xMTExMTExZW1GJ0ZALUYsNilRMFNwYWNlQ3VydmVUdXRvckYnRi9GMkY1RjhGO0Y9RmZuLUZBNjFRIihGJ0YvRjJGOEY7RkRGRkZIRkpGTEZORlBGUkZURlctRkE2MVEiKUYnRi9GMkY4RjtGREZGRkhGSkZMRk5GUEZSRlRGVy1GQTYxUSI7RidGL0YyRjhGO0ZEL0ZHRjQvRklGNy9GS0Y0RkxGTkZQRlIvRlVRJjAuMGVtRicvRlhRLDAuMjc3Nzc3OGVtRidGL0YyRjhGO0ZEVector Velocidad:use DocumentTools in
rt:=Do(%r[t]):
pxt:=Do(rt[1]);
syt:=Do(rt[2]);
tzt:=Do(rt[3]);
cvps:=Do(<pxt,syt,tzt>):
vel:=Do(diff(rt,t)):
evvel:=Do(eval(diff(rt,t),t=%t)):
rapid:=Do(Norm(eval(diff(rt,t),t=%t))):
Do(%velocidad=vel);
Do(%velocidadeval=evvel);
Do(%rap=evalf(rapid,5));
end use;
= m/s , t = s m/s , m/suse DocumentTools in
rt:=Do(%r[t]):
arcsa:=Do(arccos(eval(diff(rt[1],t),t=%t)/(Norm(eval(diff(rt,t),t=%t)))));
Do(%alfa=evalf(convert(arcsa,degrees)),5);
######################################################
arcsb:=Do(arccos(eval(diff(rt[2],t),t=%t)/(Norm(eval(diff(rt,t),t=%t)))));
Do(%beta=evalf(convert(arcsb,degrees)),5);
######################################################
arcst:=Do(arccos(eval(diff(rt[3],t),t=%t)/(Norm(eval(diff(rt,t),t=%t)))));
Do(%theta=evalf(convert(arcst,degrees)),5);
end use;
: \316\261 = , \316\262 = y \316\270 = use DocumentTools in
Do(%velocidad=NULL);
Do(%velocidadeval=NULL);
#Do(%t='NULL');
Do(%rap=NULL);
Do(%alfa=NULL);
Do(%beta=NULL);
Do(%theta=NULL);
end use;
Vector Aceleraci\303\263n:use DocumentTools in
rt:=Do(%r[t]):
pxt:=Do(rt[1]);
syt:=Do(rt[2]);
tzt:=Do(rt[3]);
cvps:=Do(<pxt,syt,tzt>):
acel:=Do(diff(rt,t$2)):
evacel:=Do(eval(diff(rt,t$2),t=%ta)):
mgacel:=Do(Norm(eval(diff(rt,t$2),t=%ta))):
Do(%aceleracion=acel);
Do(%aceleracioneval=evacel);
Do(%rapa=evalf(mgacel,5));
end use;
= m/s^2 , t = s m/s^2 , m/s^2JSFHuse DocumentTools in
rt:=Do(%r[t]):
arcsa_a:=Do(arccos(eval(diff(rt[1],t$2),t=%t)/(Norm(eval(diff(rt,t$2),t=%t)))));
Do(%alfa_a=evalf(convert(arcsa_a,degrees)),5);
######################################################
arcsb_a:=Do(arccos(eval(diff(rt[2],t$2),t=%t)/(Norm(eval(diff(rt,t$2),t=%t)))));
Do(%beta_a=evalf(convert(arcsb_a,degrees)),5);
######################################################
arcst_a:=Do(arccos(eval(diff(rt[3],t$2),t=%t)/(Norm(eval(diff(rt,t$2),t=%t)))));
Do(%theta_a=evalf(convert(arcst_a,degrees)),5);
end use;
: \316\261 = , \316\262 = y \316\270 = use DocumentTools in
Do(%aceleracion=NULL);
Do(%aceleracioneval=NULL);
#Do(%ta='NULL');
Do(%rapa=NULL);
Do(%alfa_a=NULL);
Do(%beta_a=NULL);
Do(%theta_a=NULL);
end use;
use DocumentTools in
restart:with(plots):with(LinearAlgebra):
r[t]:=Do(%r[t]):
Do(%xt=r[t][1]);
Do(%yt=r[t][2]);
Do(%zt=r[t][3]);
Do(%tt=NULL);
Do(%a_va=NULL);
Do(%Plot0=plots[display](plots[textplot]([0,0,""]),axes=none));
Do(%time(value)=0);
with(VectorCalculus):
end use;
JSFHIngrese las componentes del vector posici\303\263n: x = y = z = t = use DocumentTools in
with(plots):with(LinearAlgebra):with(VectorCalculus):
x_t:=Do(unapply(%xt,t)):
y_t:=Do(unapply(%yt,t)):
z_t:=Do(unapply(%zt,t)):
esp:=Do(spacecurve(<x_t(t), y_t(t), z_t(t)>, t=0..10,color=blue,axes=normal,labels=[x,y,z])):
vp:=Do(<x,y,z>):
vp_e:=Do(arrow(<x_t(%time),y_t(%time),z_t(%time)>,color=red)):
vel:=Do(<D(x_t)(t),D(y_t)(t),D(z_t)(t)>):
g_vel:=Do(arrow(<x_t(%time),y_t(%time),z_t(%time)>,eval(vel,t=%time),color=green)):
acel:=Do(<D(D(x_t))(t),D(D(y_t))(t),D(D(z_t))(t)>):
g_acel:=Do(arrow(<x_t(%time),y_t(%time),z_t(%time)>,eval(acel,t=%time),color="LightSeaGreen")):
vT:=Do(<D(x_t)(t),D(y_t)(t),D(z_t)(t)>/sqrt((D(x_t)(t))^2+(D(y_t)(t))^2+(D(z_t)(t))^2)):
g_T:=Do(arrow(<x_t(%time),y_t(%time),z_t(%time)>,eval(%ampT*vT,t=%time),color=black,width=0.3,head_length=.4)):
vN:=Do(<diff(vT[1],t),diff(vT[2],t),diff(vT[3],t)>/sqrt((diff(vT[1],t))^2+(diff(vT[2],t))^2+(diff(vT[3],t))^2)):
g_N:=Do(arrow(<x_t(%time),y_t(%time),z_t(%time)>,eval(%ampN*vN,t=%time),color=black,width=0.3,head_length=.4)):
vB:=Do(CrossProduct(vT,vN)):
g_B:=Do(arrow(<x_t(%time),y_t(%time),z_t(%time)>,eval(%ampB*vB,t=%time),color=yellow,width=0.3,head_length=.4)):
Do(%Plot0=display(esp,vp_e,g_vel,g_acel,g_T,g_N,g_B,scaling=constrained));
Do(%tt=%time):
v_eval:=Do(eval(vel,t=%time)):
a_eval:=Do(eval(acel,t=%time)):
alfa:=Do(arccos(DotProduct(v_eval,a_eval)/(Norm(v_eval)*Norm(a_eval)))):
Do(%a_va=evalf(convert(alfa,degrees),10));
end use;
segundosJSFHPara observar T ,N y B hay que aumentar su magnitud: (por ser unitario)*T , *N y *B Leyenda: - La curva de color az\303\272l: trayectoria. - El vector posici\303\263n: color rojo. - El vector velocidad: color verde. - El vector aceleraci\303\263n: color turquesa. - Los vectores Tangente y Normal: color negro. - El vector Binormal: color 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Angulo entre el V. velocidad y V. aceleraci\303\263n es: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
JSFH
use DocumentTools in
with(VectorCalculus):
rt:=Do(%r[t]):
rp:=Do(diff(rt,t)):
mod_rp:=Do(Norm(rp)):
T:=Do(rp/mod_rp):
Do(%resp=evalf(T,5));
#######################################
Tp:=Do(diff(T,t)):
mod_Tp:=Do(Norm(Tp)):
N:=Do(Tp/mod_Tp):
#Do(%respn=simplify(N));
Do(%respn=simplify(N));
#######################################
r2p:=Do(diff(rt,t$2)):
rp_r2p:=Do(DotProduct(rp,r2p)):
Do(%aT=simplify(rp_r2p/mod_rp));
#######################################
mod_rp_r2p:=Do(CrossProduct(rp,r2p)):
Do(%aN=Norm(mod_rp_r2p)/mod_rp);
Do(%aeval=NULL):
#######################################
Do(%ceaT=evalf(eval(%aT,t=%tc)),5);
Do(%cvT=evalf(eval(%resp,t=%tc)),5);
Do(%ceaN=evalf(eval(%aN,t=%tc)),5);
Do(%cvN=evalf(eval(%respn,t=%tc)),5);
aclt:=Do(%aT*%resp+%aN*%respn):
Do(%magac=evalf(eval(aclt,t=%tc),10));
atane:=Do(evalf(eval(%aT,t=%tc)),5):
anorme:=Do(evalf(eval(%aN,t=%tc)),5):
att:=Do(atane*T+anorme*N):
gt:=Do(Norm(att));
Do(%mvr=evalf(eval(gt,t=%tc),5));
end use;
= use DocumentTools in
r[t]:=Do(%r[t]):
rp:=Do(diff(r[t],t)):
mod_rp:=Do(Norm(rp)):
T:=Do(rp/mod_rp):
#######################################
Tp:=Do(diff(T,t)):
mod_Tp:=Do(Norm(Tp)):
N:=Do(Tp/mod_Tp):
Do(%respn=simplify(N));
#######################################
r2p:=Do(diff(r[t],t$2)):
rp_r2p:=Do(DotProduct(rp,r2p)):
Do(%aT=simplify(rp_r2p/mod_rp));
Do(%resp=NULL);
Do(%aN=NULL);
Do(%respn=NULL);
Do(%aeval=evalf(eval(%aT,t=%tc)),5);
end use;
use DocumentTools in
r[t]:=Do(%r[t]):
rp:=Do(diff(r[t],t)):
mod_rp:=Do(Norm(rp)):
T:=Do(rp/mod_rp):
Do(%resp=T);
Do(%aN=NULL);
Do(%aT=NULL);
Do(%respn=NULL);
Do(%aeval=evalf(eval(%resp,t=%tc)),5);
end use;
+ use DocumentTools in
r[t]:=Do(%r[t]):
rp:=Do(diff(r[t],t)):
mod_rp:=Do(Norm(rp)):
T:=Do(rp/mod_rp):
#######################################
Tp:=Do(diff(T,t)):
mod_Tp:=Do(Norm(Tp)):
N:=Do(Tp/mod_Tp):
Do(%respn=simplify(N));
#######################################
r2p:=Do(diff(r[t],t$2)):
rp_r2p:=Do(DotProduct(rp,r2p)):
Do(%aT=rp_r2p/mod_rp);
#######################################
mod_rp_r2p:=Do(CrossProduct(rp,r2p)):
Do(%aN=Norm(mod_rp_r2p)/mod_rp);
Do(%resp=NULL);
Do(%aT=NULL);
Do(%respn=NULL);
Do(%aeval=evalf(eval(%aN,t=%tc)),5);
end use;
use DocumentTools in
r[t]:=Do(%r[t]):
rp:=Do(diff(r[t],t)):
mod_rp:=Do(Norm(rp)):
T:=Do(rp/mod_rp):
#######################################
Tp:=Do(diff(T,t)):
mod_Tp:=Do(Norm(Tp)):
N:=Do(Tp/mod_Tp):
Do(%respn=simplify(N));
Do(%resp=NULL);
Do(%aT=NULL);
Do(%aN=NULL);
Do(%aeval=evalf(eval(%respn,t=%tc)),5);
end use;
JSFH
a = + tiempo = seg.use DocumentTools in
Do(%resp=NULL);
Do(%respn=NULL);
Do(%aT=NULL);
Do(%aN=NULL);
Do(%ceaT=NULL);
Do(%cvT=NULL);
Do(%ceaN=NULL);
Do(%cvN=NULL);
Do(%magac=NULL);
Do(%mvr=NULL);
end use;
a = + m/s^2 Vector aceleraci\303\263n = m/s^2 = m/s^2
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFH<Text-field style="Heading 1" layout="Heading 1">Curvatura y longitud de la trayectoria</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
JSFHLongitud s y curvatura kLSUnQ0FOVkFTRzYnLSUpQk9VTkRTX1hHNiMsJC0lJkZsb2F0RzYjJSlpbmZpbml0eUchIiItJSlCT1VORFNfWUdGJy0lLUJPVU5EU19XSURUSEc2IyQiJV0/Ri0tJS5CT1VORFNfSEVJR0hURzYjJCIlXT1GLS0lKUNISUxEUkVORzYsLSUlTElORUc2KC0lKE9VVExJTkVHNiMtJSZDT0xPUkc2JiUkUkdCRyQiIiFGLUZHRkctJTFMSU5FX1NUQVJUX0FSUk9XRzYjUSp2ZWUtYXJyb3c2Ii0lL0xJTkVfVEhJQ0tORVNTRzYjJCIjNUYtLSUoU1BBVElBTEc2Ji0lJlRSQU5TRzYjLSUnVkVDVE9SRzYkRkdGRy0lJ09SSUdJTkc2Iy0lJlBPSU5URzYkJCIkWCZGLSQiJCEqKUYtLSUmU0NBTEVHNiMtRlo2JEZRRlEtJSlST1RBVElPTkc2I0ZHLSUqTElORVNUWUxFRzYjRkgtJSVEQVRBRzYkNyQkIiRTJkYtJCIkIUdGLTckRl9wJCIlKzpGLS1GPjYoRkAtJS9MSU5FX0VORF9BUlJPV0dGS0ZOLUZUNiZGVi1GZ242Iy1Gam42JCQiJSs2Ri0kIiUmPiJGLUZgb0Zlb0Zoby1GXHA2JDckJCIkKyRGLSQiJSE+IkYtNyQkIiUrPkYtRmlxLSUnU1RST0tFRzYlLUZBNiMtRkQ2JkZGRkdGR0ZRLUZPNiMkIiNJRi0tRlxwNlY3JCQiJF0nRi0kIiQhekYtNyQkIiRnJ0YtJCIkIXlGLTckJCIkcSdGLSQiJHEoRi03JEZmcyQiJF0oRi03JCQiJCFvRi0kIiRTKEYtNyQkIiQhcEYtJCIkSShGLTckJCIkKyhGLSQiJD8oRi03JEZodEZodDckJCIkNShGLUZjdDckRmp0Rl50NyRGZXRGZnM3JEZgdEZhczckRlt0RlxzNyQkIiRnKEYtJCIkUydGLTckRmNzJCIkSSdGLTckJCIkKylGLSQiJDUnRi03JCQiJFMpRi0kIiQrJ0YtNyQkIiRdKUYtJCIkIWZGLTckJCIkZylGLSQiJCFlRi03JCQiJHEpRi0kIiRxJkYtNyRGXm9GY3c3JCQiJCsqRi0kIiRnJkYtNyQkIiQ/KkYtJCIkXSZGLTckJCIkSSpGLUZfcDckJCIkXSpGLSQiJEkmRi03JCQiJCEpKkYtJCIkPyZGLTckJCIlKzVGLUZbeTckJCIlSTVGLUZbeTckJCIlUzVGLSQiJDUmRi03JCQiJXE1Ri1GZnk3JCQiJSE0IkYtRmZ5NyQkIiU1NkYtRmZ5NyQkIiVJNkYtRmZ5NyQkIiVnNkYtRmZ5NyRGaXFGZnk3JCQiJT83Ri1GZnk3JCQiJV03Ri1GZnk3JCQiJWc3Ri1GW3k3JCQiJSs4Ri1GZng3JCQiJT84Ri1GZng3JCQiJWc4Ri1GX3A3JCQiJSFRIkYtRl54NyQkIiU1OUYtRml3NyQkIiVnOUYtRl53NyQkIiUhXCJGLUZedzckJCIlSTpGLUZfdjckJCIlZzpGLSQiJD8nRi03JCQiJSs7Ri1GZ3U3JCQiJUk7Ri1GZ3U3JCQiJVM7Ri1GXHM3JCQiJWc7Ri1GXHM3JCQiJXE7Ri1GXHMtRj42J0ZARk4tRlQ2JkZWLUZnbjYjLUZqbjYkJCIldjtGLSQiJEQqRi1GYG9GZW8tRmlvNiMiIiMtRlxwNiQ3JEZbXmxGYXM3JEZbXmxGaXEtRj42J0ZARk4tRlQ2JkZWLUZnbjYjLUZqbjYkJCIkbCdGLUZeeUZgb0Zlb0ZpXmwtRlxwNiQ3JEZhc0ZddjckRmFzJCIlKzdGLS0lL1RFWFRfQ09OVEFJTkVSRzYoRk4tRlQ2JkZWLUZnbjYjLUZqbjYkRl50JCIlNThGLUZgb0Zlby0lLEZJWEVEX1dJRFRIRzYjJSV0cnVlRy0lLUZJWEVEX0hFSUdIVEdGXWFsLUZccDYlNyRGaXYkIiVxNkYtNyQkIiQhPUYtRmFwJSdDTE9TRURHLSUqUEFSQUdSQVBIRzYjUWNbb1BGUmxlSFF0Wm1sbGJHUWdiM0JoY1hWbFBTSm1ZV3h6WlNJZ2MzVmljMk55YVhCMFBTSm1ZV3h6WlNJZ2RXNWtaWEpzYVc1bFBTSm1ZV3h6WlNJZ2MzVndaWEp6WTNKcGNIUTlJbVpoYkhObElpQmliMnhrUFNKbVlXeHpaU0lnWm05eVpXZHliM1Z1WkQwaVd6QXNNQ3d3WFNJZ2FYUmhiR2xqUFNKbVlXeHpaU0lnWlhobFkzVjBZV0pzWlQwaVptRnNjMlVpSUhObGJHVmpkR2x2Ymkxd2JHRmpaV2h2YkdSbGNqMGlabUZzYzJVaUlITnBlbVU5SWpFeUlpQnlaV0ZrYjI1c2VUMGlabUZzYzJVaUlHSmhZMnRuY205MWJtUTlJbHN5TlRVc01qVTFMREkxTlYwaUlIQnNZV05sYUc5c1pHVnlQU0ptWVd4elpTSWdabUZ0YVd4NVBTSlVhVzFsY3lCT1pYY2dVbTl0WVc0aUlITndZV05sWVdKdmRtVTlJakFpSUd4cGJtVmljbVZoYXowaWMzQmhZMlVpSUhKcFoyaDBiV0Z5WjJsdVBTSXdJaUJzYVc1bGMzQmhZMmx1WnowaU1DNHdJaUJwYm1sMGFXRnNQU0l3SWlCbWFYSnpkR2x1WkdWdWREMGlNQ0lnYkdWbWRHMWhjbWRwYmowaU1DSWdZblZzYkdWMGMzVm1abWw0UFNJaUlHRnNhV2R1YldWdWREMGliR1ZtZENJZ1luVnNiR1YwUFNKdWIyNWxJaUJ6Y0dGalpXSmxiRzkzUFNJd0lpQndZV2RsWW5KbFlXc3RZbVZtYjNKbFBTSm1ZV3h6WlNJK1BFWnZiblFnYjNCaGNYVmxQU0ptWVd4elpTSWdjM1ZpYzJOeWFYQjBQU0ptWVd4elpTSWdkVzVrWlhKc2FXNWxQU0ptWVd4elpTSWdjM1Z3WlhKelkzSnBjSFE5SW1aaGJITmxJaUJpYjJ4a1BTSm1ZV3h6WlNJZ1ptOXlaV2R5YjNWdVpEMGlXekFzTUN3d1hTSWdhWFJoYkdsalBTSm1ZV3h6WlNJZ1pYaGxZM1YwWVdKc1pUMGlabUZzYzJVaUlITmxiR1ZqZEdsdmJpMXdiR0ZqWldodmJHUmxjajBpWm1Gc2MyVWlJSE5wZW1VOUlqRTRJaUJ5WldGa2IyNXNlVDBpWm1Gc2MyVWlJR0poWTJ0bmNtOTFibVE5SWxzeU5UVXNNalUxTERJMU5WMGlJSEJzWVdObGFHOXNaR1Z5UFNKbVlXeHpaU0lnWm1GdGFXeDVQU0pVYVcxbGN5Qk9aWGNnVW05dFlXNGlQblE4TDBadmJuUStQQzlVWlhoMExXWnBaV3hrUGc9PUZNLUZhYGw2KEZOLUZUNiZGVi1GZ242Iy1Gam42JEZldSQiJTo5Ri1GYG9GZW9GW2FsRl9hbC1GXHA2JTckRmFzRmlgbDckJCIkKyNGLSQiJDUjRi1GaWFsLUZbYmw2I1FjW29QRlJsZUhRdFptbGxiR1FnYjNCaGNYVmxQU0ptWVd4elpTSWdjM1ZpYzJOeWFYQjBQU0ptWVd4elpTSWdkVzVrWlhKc2FXNWxQU0ptWVd4elpTSWdjM1Z3WlhKelkzSnBjSFE5SW1aaGJITmxJaUJpYjJ4a1BTSm1ZV3h6WlNJZ1ptOXlaV2R5YjNWdVpEMGlXekFzTUN3d1hTSWdhWFJoYkdsalBTSm1ZV3h6WlNJZ1pYaGxZM1YwWVdKc1pUMGlabUZzYzJVaUlITmxiR1ZqZEdsdmJpMXdiR0ZqWldodmJHUmxjajBpWm1Gc2MyVWlJSE5wZW1VOUlqRXlJaUJ5WldGa2IyNXNlVDBpWm1Gc2MyVWlJR0poWTJ0bmNtOTFibVE5SWxzeU5UVXNNalUxTERJMU5WMGlJSEJzWVdObGFHOXNaR1Z5UFNKbVlXeHpaU0lnWm1GdGFXeDVQU0pVYVcxbGN5Qk9aWGNnVW05dFlXNGlJSE53WVdObFlXSnZkbVU5SWpBaUlHeHBibVZpY21WaGF6MGljM0JoWTJVaUlISnBaMmgwYldGeVoybHVQU0l3SWlCc2FXNWxjM0JoWTJsdVp6MGlNQzR3SWlCcGJtbDBhV0ZzUFNJd0lpQm1hWEp6ZEdsdVpHVnVkRDBpTUNJZ2JHVm1kRzFoY21kcGJqMGlNQ0lnWW5Wc2JHVjBjM1ZtWm1sNFBTSWlJR0ZzYVdkdWJXVnVkRDBpYkdWbWRDSWdZblZzYkdWMFBTSnViMjVsSWlCemNHRmpaV0psYkc5M1BTSXdJaUJ3WVdkbFluSmxZV3N0WW1WbWIzSmxQU0ptWVd4elpTSStQRVp2Ym5RZ2IzQmhjWFZsUFNKbVlXeHpaU0lnYzNWaWMyTnlhWEIwUFNKbVlXeHpaU0lnZFc1a1pYSnNhVzVsUFNKbVlXeHpaU0lnYzNWd1pYSnpZM0pwY0hROUltWmhiSE5sSWlCaWIyeGtQU0ptWVd4elpTSWdabTl5WldkeWIzVnVaRDBpV3pBc01Dd3dYU0lnYVhSaGJHbGpQU0ptWVd4elpTSWdaWGhsWTNWMFlXSnNaVDBpWm1Gc2MyVWlJSE5sYkdWamRHbHZiaTF3YkdGalpXaHZiR1JsY2owaVptRnNjMlVpSUhOcGVtVTlJakV5SWlCeVpXRmtiMjVzZVQwaVptRnNjMlVpSUdKaFkydG5jbTkxYm1ROUlsc3lOVFVzTWpVMUxESTFOVjBpSUhCc1lXTmxhRzlzWkdWeVBTSm1ZV3h6WlNJZ1ptRnRhV3g1UFNKVWFXMWxjeUJPWlhjZ1VtOXRZVzRpUGpBOEwwWnZiblErUEM5VVpYaDBMV1pwWld4a1BnPT1GTS1GYWBsNihGTi1GVDYmRlYtRmduNiMtRmpuNiRGaF1sJCIlSThGLUZgb0Zlb0ZbYWxGX2FsLUZccDYlNyQkIiVxOkYtRmlxRmZhbEZpYWxGamFsLUZhYGw2KEZOLUZUNiZGVi1GZ242Iy1Gam42JEZeeCQiJHYiRi1GYG9GZW9GW2FsRl9hbC1GXHA2JTckJCIkIVxGLSQiIyEqRi03JCQiJD8iRi0kIiRxIkYtRmlhbC1GW2JsNiNRY1tvUEZSbGVIUXRabWxsYkdRZ2IzQmhjWFZsUFNKbVlXeHpaU0lnYzNWaWMyTnlhWEIwUFNKbVlXeHpaU0lnZFc1a1pYSnNhVzVsUFNKbVlXeHpaU0lnYzNWd1pYSnpZM0pwY0hROUltWmhiSE5sSWlCaWIyeGtQU0ptWVd4elpTSWdabTl5WldkeWIzVnVaRDBpV3pBc01Dd3dYU0lnYVhSaGJHbGpQU0ptWVd4elpTSWdaWGhsWTNWMFlXSnNaVDBpWm1Gc2MyVWlJSE5sYkdWamRHbHZiaTF3YkdGalpXaHZiR1JsY2owaVptRnNjMlVpSUhOcGVtVTlJakV5SWlCeVpXRmtiMjVzZVQwaVptRnNjMlVpSUdKaFkydG5jbTkxYm1ROUlsc3lOVFVzTWpVMUxESTFOVjBpSUhCc1lXTmxhRzlzWkdWeVBTSm1ZV3h6WlNJZ1ptRnRhV3g1UFNKVWFXMWxjeUJPWlhjZ1VtOXRZVzRpSUhOd1lXTmxZV0p2ZG1VOUlqQWlJR3hwYm1WaWNtVmhhejBpYzNCaFkyVWlJSEpwWjJoMGJXRnlaMmx1UFNJd0lpQnNhVzVsYzNCaFkybHVaejBpTUM0d0lpQnBibWwwYVdGc1BTSXdJaUJtYVhKemRHbHVaR1Z1ZEQwaU1DSWdiR1ZtZEcxaGNtZHBiajBpTUNJZ1luVnNiR1YwYzNWbVptbDRQU0lpSUdGc2FXZHViV1Z1ZEQwaWJHVm1kQ0lnWW5Wc2JHVjBQU0p1YjI1bElpQnpjR0ZqWldKbGJHOTNQU0l3SWlCd1lXZGxZbkpsWVdzdFltVm1iM0psUFNKbVlXeHpaU0krUEVadmJuUWdiM0JoY1hWbFBTSm1ZV3h6WlNJZ2MzVmljMk55YVhCMFBTSm1ZV3h6WlNJZ2RXNWtaWEpzYVc1bFBTSm1ZV3h6WlNJZ2MzVndaWEp6WTNKcGNIUTlJbVpoYkhObElpQmliMnhrUFNKbVlXeHpaU0lnWm05eVpXZHliM1Z1WkQwaVd6QXNNQ3d3WFNJZ2FYUmhiR2xqUFNKbVlXeHpaU0lnWlhobFkzVjBZV0pzWlQwaVptRnNjMlVpSUhObGJHVmpkR2x2Ymkxd2JHRmpaV2h2YkdSbGNqMGlabUZzYzJVaUlITnBlbVU5SWpFeUlpQnlaV0ZrYjI1c2VUMGlabUZzYzJVaUlHSmhZMnRuY205MWJtUTlJbHN5TlRVc01qVTFMREkxTlYwaUlIQnNZV05sYUc5c1pHVnlQU0ptWVd4elpTSWdabUZ0YVd4NVBTSlVhVzFsY3lCT1pYY2dVbTl0WVc0aVBuSThMMFp2Ym5RK1BDOVVaWGgwTFdacFpXeGtQZz09Rk0tRmFgbDYoRk4tRlQ2JkZWLUZnbjYjLUZqbjYkJCIlPz5GLSQiJXY4Ri1GYG9GZW9GW2FsRl9hbC1GXHA2JTckJCIlZz1GLSQiJSFIIkYtRmNlbEZpYWwtRltibDYjUWNbb1BGUmxlSFF0Wm1sbGJHUWdiM0JoY1hWbFBTSm1ZV3h6WlNJZ2MzVmljMk55YVhCMFBTSm1ZV3h6WlNJZ2RXNWtaWEpzYVc1bFBTSm1ZV3h6WlNJZ2MzVndaWEp6WTNKcGNIUTlJbVpoYkhObElpQmliMnhrUFNKbVlXeHpaU0lnWm05eVpXZHliM1Z1WkQwaVd6QXNNQ3d3WFNJZ2FYUmhiR2xqUFNKbVlXeHpaU0lnWlhobFkzVjBZV0pzWlQwaVptRnNjMlVpSUhObGJHVmpkR2x2Ymkxd2JHRmpaV2h2YkdSbGNqMGlabUZzYzJVaUlITnBlbVU5SWpFeUlpQnlaV0ZrYjI1c2VUMGlabUZzYzJVaUlHSmhZMnRuY205MWJtUTlJbHN5TlRVc01qVTFMREkxTlYwaUlIQnNZV05sYUc5c1pHVnlQU0ptWVd4elpTSWdabUZ0YVd4NVBTSlVhVzFsY3lCT1pYY2dVbTl0WVc0aUlITndZV05sWVdKdmRtVTlJakFpSUd4cGJtVmljbVZoYXowaWMzQmhZMlVpSUhKcFoyaDBiV0Z5WjJsdVBTSXdJaUJzYVc1bGMzQmhZMmx1WnowaU1DNHdJaUJwYm1sMGFXRnNQU0l3SWlCbWFYSnpkR2x1WkdWdWREMGlNQ0lnYkdWbWRHMWhjbWRwYmowaU1DSWdZblZzYkdWMGMzVm1abWw0UFNJaUlHRnNhV2R1YldWdWREMGliR1ZtZENJZ1luVnNiR1YwUFNKdWIyNWxJaUJ6Y0dGalpXSmxiRzkzUFNJd0lpQndZV2RsWW5KbFlXc3RZbVZtYjNKbFBTSm1ZV3h6WlNJK1BFWnZiblFnYjNCaGNYVmxQU0ptWVd4elpTSWdjM1ZpYzJOeWFYQjBQU0ptWVd4elpTSWdkVzVrWlhKc2FXNWxQU0ptWVd4elpTSWdjM1Z3WlhKelkzSnBjSFE5SW1aaGJITmxJaUJpYjJ4a1BTSm1ZV3h6WlNJZ1ptOXlaV2R5YjNWdVpEMGlXekFzTUN3d1hTSWdhWFJoYkdsalBTSm1ZV3h6WlNJZ1pYaGxZM1YwWVdKc1pUMGlabUZzYzJVaUlITmxiR1ZqZEdsdmJpMXdiR0ZqWldodmJHUmxjajBpWm1Gc2MyVWlJSE5wZW1VOUlqRXlJaUJ5WldGa2IyNXNlVDBpWm1Gc2MyVWlJR0poWTJ0bmNtOTFibVE5SWxzeU5UVXNNalUxTERJMU5WMGlJSEJzWVdObGFHOXNaR1Z5UFNKbVlXeHpaU0lnWm1GdGFXeDVQU0pVYVcxbGN5Qk9aWGNnVW05dFlXNGlQblE4TDBadmJuUStQQzlVWlhoMExXWnBaV3hrUGc9PUZNJSFHJSFHJSFH Ingrese el vector posici\303\263n: = m use DocumentTools in
Do(%cr_lt=NULL):
Do(%vpk=NULL):
Do(%cr_eval=NULL):
end use;
use DocumentTools in
with(VectorCalculus):
vpk[t]:=Do(%vpk):
rp_vp:=Do(diff(vpk[t],t)):
r2p_vp:=Do(diff(vpk[t],t$2)):
pc_c:=Do(CrossProduct(rp_vp,r2p_vp)):
Do(%cr_lt=simplify(Norm(pc_c)/(Norm(rp_vp))^3));
Do(%cr_eval=evalf(eval(%cr_lt,t=%tcr)),5);
Do(%ltr=NULL):
end use;
use DocumentTools in
vpk[t]:=Do(%vpk):
rp_vp:=Do(diff(vpk[t],t)):
r2p_vp:=Do(diff(vpk[t],t$2)):
pc_c:=Do(CrossProduct(rp_vp,r2p_vp)):
Do(%cr_eval=NULL):
LT:=Do(Norm(rp_vp)):
Do(%cr_lt=Int(LT,t=%t0..%tf));
Do(%ltr=int(LT,t=%t0..%tf,numeric));
end use;
m t = 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 hasta LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2KFEidEYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2MFEiPUYnRi9GNUY4L0Y8USdub3JtYWxGJy8lJmZlbmNlR0Y6LyUqc2VwYXJhdG9yR0Y6LyUpc3RyZXRjaHlHRjovJSpzeW1tZXRyaWNHRjovJShsYXJnZW9wR0Y6LyUubW92YWJsZWxpbWl0c0dGOi8lJ2FjY2VudEdGOi8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlRGL0Y1RjhGQg==s
Binormal 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JSFH Ingrese el vector r = m use DocumentTools in
Do(%magB=NULL):
Do(%BNeval=NULL):
Do(%BN=NULL):
Do(%tB=NULL):
Do(%vpN=NULL):
end use;
use DocumentTools in
vpn[t]:=Do(%vpN):
rp_vpn:=Do(diff(vpn[t],t)):
mod_rp_vpn:=Do(Norm(rp_vpn)):
TB:=Do(rp_vpn/mod_rp_vpn):
TBp:=Do(diff(TB,t)):
mod_TBp:=Do(Norm(TBp)):
NB:=Do(TBp/mod_TBp):
Do(%BN=simplify(CrossProduct(TB,NB)));
Do(%BNeval=evalf(eval(%BN,t=%tB)),5);
bneval:=Do(eval(CrossProduct(TB,NB)),t=%tB):
Do(%magB=evalf(Norm(bneval),5));
end use;
t = seg. = =