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En los extremos del hilo estan sujetas sendas particulas, de masa M la q ue se encuentra en A, y de masa m la de B. Inicialmente el hilo sobres ale por igual por ambos extremos del tubo (AC=CD=DB=b). Todo el hilo s e encuentra situado en un plano vertical DYZ, colgando verticalmente e l tramo AC, mientras que el DB esta desviado 30 grados de la vertical \+ descendente." }}}{EXCHG {PARA 202 "" 0 "" {TEXT 212 12 " Paso 0. " }{TEXT 213 93 "Reiniciaci\363n de las variables del sistema y llamada \+ a los paquetes linalg, plots y plottools." }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 214 8 "restart:" }}{PARA 202 "> " 0 "" {MPLTEXT 1 214 41 "with(linalg):with(plots):with(plottools):" }}}{EXCHG {PARA 202 "> \+ " 0 "" {MPLTEXT 1 214 23 "libname:=\"C:/\",libname;" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 214 17 "with (mecapac3d):" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 212 12 " Paso 1. " }{TEXT 213 86 "Definimos las c oordenadas generalizadas del sistema en una lista que se denominar\341 cg." }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 214 22 "cg := [theta,be ta,z] :" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 212 12 " Paso 2. " } {TEXT 213 78 "Definici\363n mediante variables de los elementos que fo rman el sistema mec\341nico." }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 214 25 "m1 := [punto,0.,-b,-z,M]:" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 214 97 "m2 := [punto,(2*b-z)*cos(beta)*sin(theta),(2*b-z)*c os(beta)*cos(theta),-((2*b-z)*sin(beta)),m]: " }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 214 45 "a1 := [segmento,[0.,-b,-z],[0.,-b,0.],blue] :" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 214 112 "a2 := [segmento, [0.,0.,0.],[(2*b-z)*cos(beta)*sin(theta),(2*b-z)*cos(beta)*cos(theta), -(2*b-z)*sin(beta)],blue]:" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 214 46 "a3 := [segmento,[0.,0.,0.],[0.,-b,0.],green] :" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 212 12 " Paso 3. " }{TEXT 213 89 "Definici \363n de la variable sistema que agrupa en una lista todos los element os anteriores." }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 214 29 "siste ma := [m1,m2,a1,a2,a3] :" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 212 12 " \+ Paso 4. " }{TEXT 213 85 "Obtenci\363n de la energ\355a cin\351tica d el sistema mediante fT asign\341ndola a la variable T." }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 214 17 "T := fT(sistema):" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 212 12 " Paso 5. " }{TEXT 213 86 "Obtenci\3 63n de la energ\355a potencial del sistema mediante fV asign\341ndola \+ a la variable V." }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 214 17 "V : = fV(sistema):" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 212 12 " Paso 6. \+ " }{TEXT 213 97 "Obtenci\363n de la lagrangiana como diferencia de ene rg\355as entre la energ\355a cin\351tica y la potencial." }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 214 19 "L := simplify(T-V):" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 212 12 " Paso 7. " }{TEXT 213 106 "Obtenci \363n de las ecuaciones de lagrange para las dos coordenadas generaliz adas mediante el operador Ec_lag" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 214 18 "ecua := ec_lag() :" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 212 12 " Paso 8. " }{TEXT 213 118 "Asignaci\363n de valores n um\351ricos a los par\341metros que queden sun asignar para poder proc eder a la integraci\363n num\351rica." }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 214 33 "m :=1 : M :=3 : b :=3 : g :=9.8 :" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 212 12 " Paso 9. " }{TEXT 213 44 "Representacion \+ de las condiciones iniciales." }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 214 34 "fG([evalf(Pi/3),evalf(Pi/4),2.]) :" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 212 13 " Paso 10. " }{TEXT 213 100 "Integraci\363n num\35 1rica del problema mediante la funci\363n fint asignando el resultado \+ a la variable res." }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 214 37 "r es := fint([0.1,0.5,0.6,0.3,1,0.9]):" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 212 13 " Paso 11. " }{TEXT 213 79 "Representaci\363n gr\341fi ca de las evoluciones temporales de theta mediante odeplot." }}} {EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 214 34 "odeplot(res,[t,theta(t)] ,0..1.64):" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 212 13 " Paso 12. " } {TEXT 213 94 "Procedemos a realizar una animaci\363n del movimiento de l conjunto por medio de la funci\363n dibu3." }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 214 16 "dibu3(1.641,20);" }}}{EXCHG {PARA 202 "> " 0 "" }}{PARA 203 "" 0 "" }{PARA 204 "" 0 "" }}{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }