Auxiliary condition

How do I solve for the auxiliary equation?

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- Jan 8th 2011, 07:40 PMdwsmithu_x-u_y+u=1

Auxiliary condition

How do I solve for the auxiliary equation? - Jan 8th 2011, 08:37 PMsnowtea
I think you made a typo, should be

but it seems to correct itself later.

You can use the inverse rotation to get your solution in terms of x and y, and then solve using the auxiliary condition.

Or you can transform the auxiliary condition into your new coordinate system. - Jan 8th 2011, 08:38 PMdwsmith
Can you show me how that is done? Yes, I made a typo.

- Jan 8th 2011, 08:51 PMsnowtea
is the line .

Taking the partial w.r.t x at y=0 for the constraint gives:

when

Take the partials. Substitute to get rid of , and solve for . - Jan 8th 2011, 08:52 PMdwsmith
- Jan 8th 2011, 08:56 PMsnowtea

implies

actually I made a mistake :p

Let me fix that. - Jan 8th 2011, 08:58 PMdwsmith
- Jan 8th 2011, 09:05 PMsnowtea
Sorry about the poor explanations :(

so

This is the same thing as the pair of constraints:

Transforming each equation gives:

Last part inside the cosine is because:

- Jan 8th 2011, 09:17 PMdwsmith
- Jan 9th 2011, 08:18 AMsnowtea
- Jan 9th 2011, 11:33 AMdwsmith
- Jan 9th 2011, 12:34 PMdwsmith
Snowtea,

unfortunately, I have no idea how to solve the problem using your method but I was able to obtain the solution.

B and D are arbitrary and since , let D = 0.

Now, let B = 1.

- Jan 9th 2011, 01:58 PMsnowtea