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M7 Mechanics Question 2 watch

1. Far easier than the first ....

2. (Original post by TeeEm)
Far easier than the first ....

Are you sure that this is right? I get an extra term of where is the conserved AM.
3. (Original post by atsruser)
Are you sure that this is right? I get an extra term of where is the conserved AM.
I hope so but these days I can never be sure

this is

conservation of AM
shape constraint
energy = constant
4. (Original post by TeeEm)
I hope so but these days I can never be sure

this is

conservation of AM
shape constraint
energy = constant
This is a rush job, so may be errors.

The initial AM .

Use cylindrical polars. We have . Taking and increasing upwards, and , we have

and E-L equations for :

(1)

(2)

(3)

Now so:

(4)

Substituting (2) into (1) gives:

(5)

and adding (4) and (5) gives:

5. (Original post by atsruser)
This is a rush job, so may be errors.

The initial AM .

Use cylindrical polars. We have . Taking and increasing upwards, and , we have

and E-L equations for :

(1)

(2)

(3)

Now so:

(4)

Substituting (2) into (1) gives:

(5)

and adding (4) and (5) gives:

shouldn't the r2 in the extra term be a2
6. (Original post by TeeEm)
shouldn't the r2 in the extra term be a2
Not as far as I can see. have already been absorbed into , so they won't appear again.
7. (Original post by atsruser)
Not as far as I can see. have already been absorbed into , so they won't appear again.
I cannot see anything wrong with you ... maybe I got it wrong
will check my solution before I post
8. (Original post by atsruser)
Not as far as I can see. have already been absorbed into , so they won't appear again.
I found what is happening we are both correct ...
Stupidity on my part ...
the extra bit is a function or r, which I absorbed into the potential, rellabelling as f(r), forgetting I had already used it to describe the equation of the curve
9. my solution
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