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En el disco existe una acanaladura radial sin masa y lisa por la que desliza una r\363tula cil\355ndrica de masa m, que a su vez es el punto de suspensi\363n de un p\351ndulo simple de \+ longitud l y masa m. La r\363tula act\372a obligando al p\351ndulo a m overse en el plano vertical que contiene a la acanaladura." }}}{EXCHG {PARA 205 "" 0 "" {TEXT 218 12 " Paso 0. " }{TEXT 217 93 "Reiniciac i\363n de las variables del sistema y llamada a los paquetes linalg, p lots y plottools." }}}{EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 219 8 "res tart:" }}}{EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 219 41 "with(linalg):w ith(plots):with(plottools):" }}}{EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 219 94 "libname:=\"F:/Documents and Settings/ruper/Mis documentos/Area DeMecanica/BecaMecapac/\",libname;" }}}{EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 219 16 "with(mecapac3d):" }}}{EXCHG {PARA 205 "" 0 "" {TEXT 218 12 " Paso 1. " }{TEXT 217 86 "Definimos las coordenadas g eneralizadas del sistema en una lista que se denominar\341 cg." }}} {EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 219 18 "cg:=[phi,theta,s];" }}} {EXCHG {PARA 205 "" 0 "" {TEXT 218 12 " Paso 2. " }{TEXT 217 78 "De finici\363n mediante variables de los elementos que forman el sistema \+ mec\341nico." }}}{EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 219 42 "rotula: =[punto,s*cos(phi),s*sin(phi),0,m]:" }}}{EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 219 82 "punt:=[punto,(s+l*sin(theta))*cos(phi),(s+l*sin(the ta))*sin(phi),-l*cos(theta),m]:" }}}{EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 219 12 "xg:=[0,0,0]:" }}}{EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 219 18 "roti:=rota(phi,3):" }}}{EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 219 26 "disc:=[disco,xg,roti,M,R]:" }}}{EXCHG {PARA 205 "" 0 "" {TEXT 218 12 " Paso 3. " }{TEXT 217 75 "Definici\363n de los e lementos gr\341ficos que definiran nuestro sistema de ejes." }}} {EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 219 55 "aphi:=[angulo,[1,0,0],[0 ,0,0],[cos(phi),sin(phi),0],1]:" }}}{EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 219 134 "atheta:=[angulo,[s*cos(phi),s*sin(phi),-1],[s*cos( phi),s*sin(phi),0],[(s+sin(theta))*cos(phi),(s+sin(theta))*sin(phi),-c os(theta)],1]:" }}}{EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 219 56 "aca:= [segmento,[0,0,0],[R*cos(phi),R*sin(phi),0],black]:" }}}{EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 219 114 "var:=[segmento,[s*cos(phi),s*sin(phi ),0],[(s+l*sin(theta))*cos(phi),(s+l*sin(theta))*sin(phi),-l*cos(theta )],red]:" }}}{EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 219 37 "ejeX:=[vect or,[0,0,0],[R+2,0,0],red]:" }}}{EXCHG {PARA 206 "> " 0 "" {MPLTEXT 1 220 39 "ejeY:=[vector,[0,0,0],[0,R+2,0],green]:" }}}{EXCHG {PARA 207 " > " 0 "" {MPLTEXT 1 221 38 "ejeZ:=[vector,[0,0,0],[0,0,R+2],blue]:" }} }{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 221 26 "TO := [texto,[0,1,0],\" O\"]:" }}}{EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 219 14 "TX := [texto,[ " }{MPLTEXT 1 219 3 "R+3" }{MPLTEXT 1 219 11 ",0,0],\"X\"]:" }}} {EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 221 28 "TY := [texto,[0,R+3,0], \"Y\"]:" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 221 28 "TZ := [texto ,[0,0,R+3],\"Z\"]:" }}}{EXCHG {PARA 205 "" 0 "" {TEXT 218 12 " Paso 4. " }{TEXT 217 89 "Definici\363n de la variable sistema que agrupa e n una lista todos los elementos anteriores." }}}{EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 219 75 "sistema:=[punt,rotula,disc,aca,var,atheta,aphi ,ejeX,ejeY,ejeZ,TO,TX,TY,TZ]:" }}}{EXCHG {PARA 205 "" 0 "" {TEXT 218 12 " Paso 5. " }{TEXT 217 85 "Obtenci\363n de la energ\355a cin\351 tica del sistema mediante fT asign\341ndola a la variable T." }}} {EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 219 15 "T:=fT(sistema);" }}} {EXCHG {PARA 205 "" 0 "" {TEXT 218 12 " Paso 6. " }{TEXT 217 86 "Ob tenci\363n de la energ\355a potencial del sistema mediante fV asign\34 1ndola a la variable V." }}}{EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 219 15 "V:=fV(sistema);" }}}{EXCHG {PARA 205 "" 0 "" {TEXT 218 12 " Pas o 7. 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Obtenci\363n de la s ecuaciones de lagrange para las dos coordenadas generalizadas median te el operador Ec_lag" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 221 15 "ecua:=ec_lag();" }}}{EXCHG {PARA 207 "" 0 "" {TEXT 222 11 " Pas o 9." }{TEXT 223 119 " Asignaci\363n de valores num\351ricos a los par \341metros que queden sun asignar para poder proceder a la integraci\3 63n num\351rica." }}}{EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 219 32 "R:= 3: l:=2 :m:=5: M:=10: g:=9.8:" }}}{EXCHG {PARA 205 "" 0 "" {TEXT 218 12 " Paso 10." }{TEXT 217 101 " Integraci\363n num\351rica del prob lema mediante la funci\363n fint asignando el resultado a la variable \+ res." }}}{EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 219 43 "res:=fint([1.0, evalf(Pi/8),1.0,1.0,0.0,0]):" }}}{EXCHG {PARA 205 "> " 0 "" {MPLTEXT 1 219 9 "res(0.1):" }}}{EXCHG {PARA 205 "" 0 "" {TEXT 218 13 " Paso 11. 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