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Lagrange's Mechanics

  1. Apr 13, 2016 #1
    1. The problem statement, all variables and given/known data
    Find the differential equations of motion of a projectile in a uniform gravitational field without
    air resistance.

    2. Relevant equations
    For the motion of a projectile,
    in horizontal, sx = ux t
    in vertical, sy = uy t + 1/2 gt2
    KE = 1/2 mv2
    PE = mgh

    3. The attempt at a solution
    L = KE - PE
    = 1/2 m ( vx2 + vy2 ) - mgy
    Then find their partial differentiation in terms of x, x_dot, y and y_dot.

    However, the answer claims that there is z-direction motion.
    Why z direction takes into the case?
    Thankyou.
     
  2. jcsd
  3. Apr 13, 2016 #2
    if there is a general motion of projectile i.e. there are velocities in x,y,z directions at t=0 one can have equations of motion.
    first one must choose the direction of gravitational field and a natural choice will be z.
     
  4. Apr 15, 2016 #3
    Thanks I got the idea
     
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