Constant phase traces on a Nyquist plot: how?

I know how to trace closed-loop transfer function constant magnitude curves on a Nyquist plot.
I have not yet been able to find a geometric construct to trace
closed-loop transfer function constant phase curves. I know these curves are perpendicular to the constant magnitude curves (why?).
Given M a point on the open-loop transfer function, O the origin, and A the point (-1, j0), arg(OM) - arg(AM) = constant should do it. Alas, it leads me nowhere.
Could you give me some tips?
Thank you very much in advance.
--
Jean Castonguay
Électrocommande Pascal
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I don't have this at home, but I do have the equations for M and N circles for inverse Nyquist diagrams M being circles of constant magnitude or gain, and N being circles of constant phase:
u/y = X + 1 + jY M = | u / y |
1/M = SQRT [ (X+1)^2 + Y^2 ] 1/M^2 = (X+1)^2 + Y^2 Circle with centre at X=-1, Y=0, and radius r = 1/M
Lines of constant phase for the INVERSE Nyquist diagram are given by: alpha = /_ u / y = -tan^-1 ( Y / (X+1))
Hope this helps. I'll see if I can find the normal (not inverse) stuff tomorrow.
I used to have a classical control theory by Atkinson with this in. Loaned it to a colleague.

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Yes, how many excellent books have we lost by lending them to colleagues!?
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