- #1
Odious Suspect
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I posted a question about this yesterday, but realized I had made a stupid mistake in my derivation.
Orbital dynamics: "The familiar arc-cosine form"
That error has been corrected. I still have a deeper question. I believe this expression can be developed using the geometry of an ellipse in a way which adds insight into the original physics where it is being applied.
Some 30 odd years ago I saw something of this nature done in an introductory physics course.
Is anybody here familiar with such a development?
$$-\int \frac{1}{\sqrt{a+2 bx-hx^2}} \, dx=\frac{1}{\sqrt{h}}\arccos \left[\frac{b-hx}{\sqrt{a+b^2h}}\right]$$
Orbital dynamics: "The familiar arc-cosine form"
That error has been corrected. I still have a deeper question. I believe this expression can be developed using the geometry of an ellipse in a way which adds insight into the original physics where it is being applied.
Some 30 odd years ago I saw something of this nature done in an introductory physics course.
Is anybody here familiar with such a development?
$$-\int \frac{1}{\sqrt{a+2 bx-hx^2}} \, dx=\frac{1}{\sqrt{h}}\arccos \left[\frac{b-hx}{\sqrt{a+b^2h}}\right]$$