Lagrangian and Hamiltonian equations of motion

[bnz23]

Homework Statement

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

Homework 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

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!

 

[tman12321]

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.

 

[bnz23]

Thank you! That did it. All solved.