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Lagrange's Mechanics

  • Thread starter YauYauYau
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  • #1
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Homework Statement


Find the differential equations of motion of a projectile in a uniform gravitational field without
air resistance.

Homework 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

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.
 

Answers and Replies

  • #2
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However, the answer claims that there is z-direction motion.
Why z direction takes into the case?
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.
 
  • #3
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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.
Thanks I got the idea
 

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