# MTW Exercise 6.9

1. Oct 9, 2014

### TerryW

Can anyone help with the attached problem. A simple yes or no answer only is required, but if you want to point me in a particular direction......

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2. Oct 9, 2014

### Staff: Mentor

The three equations in the attachment represent a coupled system of three differential equations. There are not three variables - there are six, the three variables and the three derivatives of these variables.

Since the question is more about solving a system of differential equations, and less about relativity, I am moving the thread to the technical math section.

Last edited: Oct 9, 2014
3. Oct 9, 2014

### TerryW

I think you have answered my question. Thanks

Last edited by a moderator: Oct 9, 2014
4. Oct 9, 2014

### dextercioby

You have both t and tau. Did you mean to write only 1 variable?

5. Oct 9, 2014

### Staff: Mentor

I noticed that as well. My guess is that it should be one of them, not both.

6. Oct 10, 2014

### TerryW

The equations are correct and do include both t and tau, but this works out OK because dt/d(tau) = gamma

Don't bother to spend any more time on this - the message is clear that I have six variables and only three equations so I have to 'take a guess' at what the solutions may be.

TerryW

7. Oct 10, 2014

### Staff: Mentor

8. Oct 14, 2014

### lpetrich

I looked at this problem, and I suggest turning the S's into these combinations: S0, (S1*cos(ω*t)+S2*sin(ω*t)), (-S1*sin(ω*t)+S2*cos(ω*t)), or reversed signs for sin(ω*t) if necessary. You will find three differential equations for them. Since the coefficients are constant, you can easily make them vary as exp(λ*τ), where you must find λ.

9. Oct 24, 2014

### HallsofIvy

You switched symbols in the middle of the equations. Are we to assume that "S1" is the same as "S1", etc.?

10. Oct 24, 2014

### TerryW

In this case, S1 = η11S1.

As I said in my reply to Dextercioby and Mark44, the answer telling me that I have 6 variable was all I needed, so please don't worry about this any further on my behalf.

Regards

TerryW