• Support PF! Buy your school textbooks, materials and every day products Here!

Central Motion Problem

  • #1

Homework Statement



Consider an isotropic harmonic oscillator whose potential is given by V(r)=0.5kr^2. Calculate the value of r(t) for the orbit of a particle.


Homework Equations



dr/dt=[tex]\sqrt{2/m(E-0.5kr^2-L^2/2mr^2)}[/tex] (call the right side of the eqn 'stuff')



The Attempt at a Solution



I'm unable to solve the integral [tex]\int[/tex][tex]\frac{dr}{stuff}[/tex] as is.
I'm sure there's a subsitution or some other trick I can do to make the integral solvable but I can't figure it out =/
 

Answers and Replies

  • #2
diazona
Homework Helper
2,175
6
Note that when you separate the equation, you'll get a fraction within a fraction:
[tex]\frac{\mathrm{d}r}{\sqrt{\cdots + A/r^2}} = \cdots[/tex]
It's usually a good idea to simplify such expressions like so:
[tex]\frac{\mathrm{d}r}{\sqrt{\frac{1}{r^2}(\cdots + A)}} = \cdots[/tex]
so that you're left with a regular polynomial times some overall factor. With a couple more steps, you can get that into a form where you can use the substitution [itex]u = r^2[/itex].
 

Related Threads for: Central Motion Problem

Replies
0
Views
5K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
1K
Replies
1
Views
1K
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
4
Views
779
  • Last Post
Replies
2
Views
3K
Top