(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose the potential in a problem of one degree of freedom is linearly dependent on time such that the Hamiltonian has the form:

H= p^2/2m - mAtq

where m is the mass of the object and A is contant

Using Hamilton's canonical equations that are give below. Find the equations of motion and obtain the solution by integrating directly.

2. Relevant equations

q(dot) = ∂H/∂p

-p(dot) = ∂H/∂q

3. The attempt at a solution

Finding q(dot) = ∂H/∂p = p/m → integrating q=q(knot) + pt/m

Finding p(dot) = -∂H/∂q = -(-mAt) → integrating p= p(knot) +mAt^2/2

the initial conditions were p(knot)= p and q(knot) = q at t=0

Subbing the expression for p into the formula for q

q= q(knot) + [p(knot) + mAt^2/2]*t/m = q(knot) + p(knot)t/m + 1/2*(At^3)

The solution I obtained for my expression for q does not match the desired that was given by my professor of q(knot) + p(knot)t/m + 1/6*(At^3).

I am trying to determine if I made a mistake somewhere. It appears to me that my solution is correct. Any guidance would be greatly appreciated.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Use Hamiltons canonical equations and integrate them to find expressions for q and p

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