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masa m2 y radio R. Dicho disco se haya ensartado en un ej e vertical en su punto central. Los unicos movimientos permitidos para el disco son la rotacion a traves de su eje y una translacion vertica l." }}{PARA 209 "" 0 "" }{PARA 209 "" 0 "" {TEXT 216 132 "El disco pos ee una velocidad de rotacion constante y se encuentra unido con el ori gen de coordenadas por medio de un resorte lineal." }}{PARA 209 "" 0 " " }}{EXCHG {PARA 209 "" 0 "" {TEXT 216 4 " " }{TEXT 217 7 "Paso 0." }{TEXT 216 94 " Reiniciaci\363n de las variables del sistema y llamad a a los paquetes linalg, plots y plottools." }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 218 8 "restart:" }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 218 41 "with(linalg):with(plots):with(plottools):" }}} {EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 218 23 "libname:=\"C:/\",libname ;" }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 218 16 "with(mecapac3d):" }}}{EXCHG {PARA 209 "" 0 "" {TEXT 216 4 " " }{TEXT 217 7 "Paso 1." }{TEXT 216 87 " Definimos las coordenadas generalizadas del sistema en una lista que se denominar\341 cg." }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 218 18 "cg:=[theta,phi,z];" }}}{EXCHG {PARA 209 "" 0 "" {TEXT 216 4 " " }{TEXT 217 7 "Paso 2." }{TEXT 216 79 " Definici\363 n mediante variables de los elementos que forman el sistema mec\341nic o." }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 218 84 "m1:=[punto,(R+l*s in(theta))*cos(phi),(R+l*sin(theta))*sin(phi),-(z+l*cos(theta)),m];" } }}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 218 38 "d1:=[disco,[0,0,-z],ro ta(phi,3),m2,R];" }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 218 118 "l1 :=[segmento,[R*cos(phi),R*sin(phi),-z],[(R+l*sin(theta))*cos(phi),(R+l *sin(theta))*sin(phi),-(z+l*cos(theta))],red];" }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 218 40 "muelle1:=[muelle,[0,0,0],[0,0,-z],k,l0];" } }}{EXCHG {PARA 209 "" 0 "" {TEXT 216 4 " " }{TEXT 217 7 "Paso 3." } {TEXT 216 76 " Definici\363n de los elementos gr\341ficos que definira n nuestro sistema de ejes." }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 218 36 "ejex:=[vector,[0,0,0],[10,0,0],red]:" }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 218 38 "ejey:=[vector,[0,0,0],[0,10,0],green]:" }}} {EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 218 37 "ejez:=[vector,[0,0,0],[0 ,0,10],blue]:" }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 218 27 "TO := \+ [texto,[0,0,-1],\"O\"]:" }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 218 27 "TX := [texto,[10,0,1],\"X\"]:" }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 218 27 "TY := [texto,[0,10,1],\"Y\"]:" }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 218 27 "TZ := [texto,[0,0,10],\"Z\"]:" }}}{EXCHG {PARA 209 "" 0 "" {TEXT 216 4 " " }{TEXT 217 7 "Paso 4." }{TEXT 216 90 " Definici\363n de la variable sistema que agrupa en una lista \+ todos los elementos anteriores." }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 218 55 "sistema:=[m1,d1,l1,muelle1,ejex,ejey,ejez,TO,TX,TY, TZ]:" }}}{EXCHG {PARA 209 "" 0 "" {TEXT 216 4 " " }{TEXT 217 7 "Pas o 5." }{TEXT 216 86 " Obtenci\363n de la energ\355a cin\351tica del si stema mediante fT asign\341ndola a la variable T." }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 218 15 "V:=fV(sistema);" }}}{EXCHG {PARA 209 "" 0 "" {TEXT 216 4 " " }{TEXT 217 7 "Paso 6." }{TEXT 216 87 " Obte nci\363n de la energ\355a potencial del sistema mediante fV asign\341n dola a la variable V." }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 218 15 "T:=fT(sistema);" }}}{EXCHG {PARA 209 "" 0 "" {TEXT 216 4 " " } {TEXT 217 7 "Paso 7." }{TEXT 216 98 " Obtenci\363n de la lagrangiana c omo diferencia de energ\355as entre la energ\355a cin\351tica y la pot encial." }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 218 17 "L:=simplify( T-V);" }}}{EXCHG {PARA 209 "" 0 "" {TEXT 216 4 " " }{TEXT 217 7 "Pa so 8." }{TEXT 216 107 " Obtenci\363n de las ecuaciones de lagrange par a las dos coordenadas generalizadas mediante el operador Ec_lag" }}} {EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 218 29 "ecua:=map(simplify,ec_la g());" }}}{EXCHG {PARA 209 "" 0 "" {TEXT 216 4 " " }{TEXT 217 7 "Pa so 9." }{TEXT 216 119 " Asignaci\363n de valores num\351ricos a los pa r\341metros que queden sun asignar para poder proceder a la integraci \363n num\351rica." }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 218 40 "R :=6:l:=3:m:=4:m2:=4:g:=9.8:k:=50:l0:=0:" }}}{EXCHG {PARA 209 "" 0 "" {TEXT 216 4 " " }{TEXT 217 8 "Paso 10." }{TEXT 216 101 " Integraci \363n num\351rica del problema mediante la funci\363n fint asignando e l resultado a la variable res." }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 218 28 "res:=fint([0,10,0,10,0,10]);" }}}{EXCHG {PARA 209 " " 0 "" {TEXT 216 4 " " }{TEXT 217 8 "Paso 11." }{TEXT 216 101 " Rep resentaci\363n gr\341fica de las evoluciones temporales de la evoluci \363n temporal de z mediante odeplot." }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 218 46 "odeplot(res,[t,theta(t)],0..30,numpoints=100);" }}} {EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 218 44 "odeplot(res,[t,phi(t)],0 ..30,numpoints=100);" }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 218 42 "odeplot(res,[t,z(t)],0..30,numpoints=100);" }}}{EXCHG {PARA 209 "" 0 "" {TEXT 216 4 " " }{TEXT 217 8 "Paso 12." }{TEXT 216 95 " Procedem os a realizar una animaci\363n del 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