{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 353 " restart; with(plot s):\n Su2 := K=tan(1/2*psi), psi=146/180*Pi, phi=108/180*Pi, Xv=2,\n \+ Yv=-0.18, s=[0.1, 0.3, 1.085], S=1.3, h=0.4;\n HP := x^2/a^2-y^2 /b^2=1:\n HP := simplify(map(u->(u-1)*b^2,HP)):\n HP := simplify(subs( b=K*a,HP)):\n HPR := subs([x=x*cos(phi)+y*sin(phi),\n y=- x*sin(phi)+y*cos(phi)],HP):\n HPRS := subs(x=x-Xv,y=y-Yv,HPR);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 " assign(Su2);\n F := expand( evalf(lhs(HPRS)));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 222 " x1 \+ := Xv-1; x2 := Xv+0.15; y1 := Yv-0.02; y2 := 0;\n AP[12] := implicitpl ot([seq(F, a=1/100*[$1..10])], x=x1..x2,\n y=y1..y2, labels= [\"x [m]\",\"y [m]\"], grid=[60, 60],\n thickness=[4, seq(1, i=2..10)]): %;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 " read \" drive.sav\":\n a := 0.01; dT := a/v; N := ceil(Tf/dT*2); T := Tf/N*[$0 ..N]:\n N := nops(T);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 432 " \+ Gx := map(u->evalf(subs(t=u, Gx)), T):\n Gy := map(u->evalf(subs(t=u, \+ Gy)), T):\n Gxt := map(u->evalf(subs(t=u, Gxt)),T):\n Gyt := map(u->ev alf(subs(t=u, Gyt)), T):\n Gxtt := map(u->evalf(subs(t=u, Gxtt)), T): \n Gytt := map(u->evalf(subs(t=u, Gytt)), T):\n Fx := unapply(diff(F, \+ x), x, y);\n Fy := unapply(diff(F, y), x, y);\n Fxx := unapply(diff(F, x, x), x, y);\n Fyy := unapply(diff(F, y, y), x, y);\n Fxy := unapply (diff(F, x, y), x, y);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 " \+ read \"Functions.sav\":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 " Dxy:=(Gx[2]-Gx[1])*2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 " position := subs(fsolve(\{(Gx[1]-x)^2+(Gy[1]-y)^2=S^2, F\},\n \+ \{x, y\}, \{x=x1..x2, y=y1..y2\}), [x, y]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 317 " Hx[1] := position[1]: Hy[1] := position[2] :\n for i from 2 to N do;\n position := subs(fsolve(\{(Gx[i]-x)^2+(G y[i]-y)^2=S^2, F\},\n \{x, y\}, \{x=Hx[i-1]-Dxy..Hx[i-1]+Dxy,\n \+ y=Hy[i-1]-Dxy..Hy[i-1]+Dxy\}), [x, y]);\n Hx[i] := position[1]: \n Hy[i] := position[2]:\n if i mod 25 = 0 then print(i) end if;\n end do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 " plot([seq([Hx[ i], Hy[i]], i=1..N)]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 740 " read \"plots.sav\":\n Hxt := [seq(Vx(Gx[i], Gy[i], Gxt[i], Gyt[i], Hx [i], Hy[i]),\n i=1..N)]:\n Hyt := [seq(Vy(Gx[i], Gy[i], Gxt[i], Gyt[i], Hx[i], Hy[i]),\n i=1..N)]:\n pl1 := plot(zip((u, v)->[ u, v], Hxt, Hyt), color=grey,\n thickness=3):\n AP[13] := displ ay(\{PL1, pl1\},\n labels=[\"Vx [m/s]\", \"Vy [m/s]\"]): %; \n Hxtt := [seq(Ax(Gx[i], Gy[i], Gxt[i], Gyt[i], Gxtt[i], Gytt[i],\n \+ Hx[i], Hy[i], Hxt[i], Hyt[i]), i=1..N)]:\n Hytt := [seq( Ay(Gx[i], Gy[i], Gxt[i], Gyt[i], Gxtt[i], Gytt[i],\n H x[i], Hy[i], Hxt[i], Hyt[i]), i=1..N)]:\n pl2 := plot(zip((u,v)->[u, v ], Hxtt, Hytt), color=grey,\n thickness=3):\n AP[14] := display (\{PL2, pl2\},\n labels=[\"Ay [m/s^2]\", \"Ay [m/s^2]\"]): % ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 389 " Ex := (x(t)-X(t))/S; Ey := (y(t)-Y(t))/S;\n for i from 1 to 3 do;\n Px[i] := X(t)+Ex*s[i ]+Ey*h; Py[i] := Y(t)+Ey*s[i]-Ex*h;\n Vx[i] := diff(Px[i], t); \+ Vy[i] := diff(Py[i], t);\n Ax[i] := diff(Vx[i], t); Ay[ i] := diff(Vy[i], t);\n V[i] := sqrt(Vx[i]^2+Vy[i]^2); A[i] := sqrt (Ax[i]^2+Ay[i]^2);\n At[i] := diff(V[i],t); An[i] := sqrt(A [i]^2-At[i]^2);\n end do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 271 " i := 'i':\n SU := [diff(X(t),t,t)=Gxtt[i], diff(X(t),t)=Gxt[i], \+ X(t)=Gx[i],\n diff(Y(t),t,t)=Gytt[i], diff(Y(t),t)=Gyt[i], Y(t) =Gy[i],\n diff(x(t),t,t)=Hxtt[i], diff(x(t),t)=Hxt[i], x(t)=Hx[ i],\n diff(y(t),t,t)=Hytt[i], diff(y(t),t)=Hyt[i], y(t)=Hy[i]]: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 325 " AP[15] := plot([seq([ seq(subs(SU, [T[i], At[j]]), i=1..N)],\n j=1..3)], color=bla ck, thickness=[3, 2, 1],\n labels=[\"t [s]\", \"At [m/s^2]\" ]): %;\n AP[16] := plot([seq([seq(subs(SU, [T[i], An[j]]), i=1..N)],\n j=1..3)], color=black, thickness=[3, 2, 1],\n lab els=[\"t [s]\", \"An [m/s^2]\"]): %;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 135 " for j from 12 to 16 do;\n plotsetup(ps, plotoutp ut=cat(ap, j, `.ps`),\n plotoptions=`landscape, noborder`);\n \+ AP[j];\n end do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "17" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }