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Lagrangian and Hamiltonian equations of motion

  1. Mar 16, 2014 #1
    1. The problem statement, all variables and given/known data
    To try and relate the three ways of calculating motion, let's say you have a particle of some mass, completely at rest, then is acted on by some force, where F equals a constant, C, times time. (C*t).
    I want to find the equations of motion using Lagrangrian, but also Newton and Hamilton

    2. Relevant equations
    I know I need L= T - V
    T = 1/2mv^2, where v is x dot
    This needs to be altered for the Force equation
    I feel PE (V) is just mvx



    3. The attempt at a solution
    Then if these T and V are correct, I need to solve the DE for Lagrange. That is easy once I know my L equation is correct.
    Next, Hamilton.

    How would this be done with Newton's equations of motion? Simple I'm sure.

    Thanks!
     
  2. jcsd
  3. Mar 17, 2014 #2
    If you're working in one dimension, Newton's second law is just m a = C t, where a is the acceleration. Since F = -dU/dx, we can choose U = - C t x. Then L = 1/2 m v^2 + C t x, and H = 1/2 m v^2 - C t x.
     
  4. Mar 17, 2014 #3
    Thank you! That did it. All solved.
     
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