Solution
Found the solution.
If anyone passes by:
Write S = W(x) + W(t)x + f(t)
and calculate (dS/dx) and then square it.
Set up and solve for terms just contaoing x and then the ones containing t.
And with initial conditions you obtain the solution.
I am currently taking a course in classical mechanics and my professor have handed out a lot of problems, some with solution.
But how do you solve the S(x,t)=X(x)T(t) in this case.
Remeber its (dS/dx)^2 and thus yields: (dX/dx)^2T^2
And the term containing both x and t..?
Should it go...
Thanks for the tip, but I am just having a problem with that..
its -mAxt, so its a function of both x and t.
I have the solution:
S = x(alpha) + 0.5 mAxt^2 + (1/40)mA^2 t^5 - (1/6)A(alpha)t^3 - (1/2m)(alpha)^2t
I am really at lost in this problem.
(1/2m)(dS/dx)^2 - mAxt + dS/dt = 0, where all d are partial derivatives
This should be the correct equation, but how to solve it?
Supposedly this is a case where you don't have to separate t
(Goldstein, 445 and prob 8 479, third edition)
But I still...
Hello
I am having a litte problem solving h=[ p^2 / (2m) ] + mAxt
where m, A are constants. initial conditions: t=0, x=0, p= mv
Supposedly sol this with Hamiltons principal function.
A hint for start would be nice
Thanks in Advance