Angle ψ Between the Ellipse Axis and the x-Axis

Finally nailed the derivation for the angle ψ that an ellipse's major axis makes with the x-axis — posting it because nobody else seems to have one up.

Back when I was in the lower grades…

Figure for Angle ψ Between the Ellipse Axis and the x-Axis

Figure for Angle ψ Between the Ellipse Axis and the x-Axis

when there’s an ellipse like this,

about the relation for the angle psi that the major axis makes with the x-axis;;;;;

the classical mechanics textbook

Figure for Angle ψ Between the Ellipse Axis and the x-Axis

had written it like this, and I realized while moving that posting over to English that I hadn’t properly derived it back then T_T T_T T_T T_T

Well… anyway, today I did manage to do it.

The reason I’m bothering to put up a posting is that a lot of people ask about this,

but a posting with the derivation doesn’t seem to come up in searches, so I’m putting one up….

Actually, I don’t think what I worked out is the standard approach,

and I’m sure there has to be an easier method,

but anyway, I did prove it T_T T_T T_T

Sigh…

Figure for Angle ψ Between the Ellipse Axis and the x-Axis

Figure for Angle ψ Between the Ellipse Axis and the x-Axis

Figure for Angle ψ Between the Ellipse Axis and the x-Axis

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