Help with MTW Exercise 6.9 - Yes/No Answer

[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...

 

[Mark44]

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.

 

[TerryW]

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.

I think you have answered my question. Thanks

 

[dextercioby]

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

 

[Mark44]

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

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

 

[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

 

[Mark44]

There's a more systematic way of solving systems of linear differential equations. Here's a link to the intro page for a set of pages that discuss this technique - http://tutorial.math.lamar.edu/Classes/DE/SystemsIntro.aspx.

 

[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.

 

[HallsofIvy]

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

 

[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.RegardsTerryW