Download Mecanica Clasica Avanzada by Jorge MAHECHA GÓMEZ PDF

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During this e-book, in Spanish, are defined in transparent and whole way
several difficulties of statics, mechanics, kinematics, dynamics and
analytical dynamics. contains non traditional matters like
perturbation concept, Kepler challenge in parabolic coordinates, and
connection with quantum mechanics.

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Extra info for Mecanica Clasica Avanzada

Example text

140) las fuerzas de reacci´on de las ligaduras. Fuerzas derivables de un potencial. 118), las fuerzas generalizadas tomar´an la forma: Q(a) ν =− ∂ V (q, t) ; ∂qν ν = 1, 2, ... 181) se pueden escribir: ∂ d ∂(T − V ) − (T − V ) = 0 dt ∂ q˙ν ∂qν ν = 1, 2, ... 183) T en coordenadas generalizadas depende de (q), (q) ˙ y de t en el caso en que las ligaduras sean re´ onomas. 184) Entonces las ecuaciones de movimiento para un sistema hol´ onomo con fuerzas derivables de un potencial que no depende de las velocidades son: d ∂L ∂L − = 0; dt ∂ q˙ν ∂qν ν = 1, 2, ...

La soluci´on de un problema de est´ atica consiste en hallar la configuraci´on de equilibrio (xi , zi , yi para i = 1, 2, ... N ), y las fuerzas de reacci´on de las ligaduras (Rxi , Ryi , Rzi para i = 1, 2, ... N ). Son seis inc´ ognitas que se obtienen resolviendo simult´ aneamente las siguientes ecuaciones algebraicas: (a) Fi + Ri = 0 ; i = 1, 2, ... 54) fα (r1 , r2 , ... rN ) = 0 ; α = 1, 2, ... 53) son 3N ecuaciones que determinan las Ri . Para hallar la configuraci´on de equilibrio basta resolver las ecuaciones: N (a) Fi i=1 · δri = 0 y fα (r1 , r2 , ...

Esta ecuaci´ on establece lo siguiente: “en todo instante en un sistema din´amico la suma de (a) las fuerzas efectivas Fi y de las fuerzas de inercia −mi r¨i no realiza trabajo al efectuar desplazamientos virtuales del sistema”, o m´as en general establece que: “la ecuaci´ on general de la din´ amica expresa una condici´on necesaria y suficiente para que un movimiento compatible con las ligaduras sea a la vez compatible con las fuerzas aplicadas”. Esta ecuaci´ on es aplicable a cualquier sistema ideal, hol´ onomo o no hol´ onomo.

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