I posted a question about this yesterday, but realized I had made a stupid mistake in my derivation.(adsbygoogle = window.adsbygoogle || []).push({});

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?

$$-\int \frac{1}{\sqrt{a+2 bx-hx^2}} \, dx=\frac{1}{\sqrt{h}}\arccos \left[\frac{b-hx}{\sqrt{a+b^2h}}\right]$$

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Deriving this "familiar arccosine form" of integral

Tags:

Loading...

Similar Threads - Deriving familiar arccosine | Date |
---|---|

I Derivative and Parameterisation of a Contour Integral | Feb 7, 2018 |

I Why does this concavity function not work for this polar fun | Jan 26, 2018 |

I Euler Lagrange formula with higher derivatives | Jan 24, 2018 |

I Derivative of infinitesimal value | Jan 15, 2018 |

Anyone familiar with fractals? | Dec 8, 2011 |

**Physics Forums - The Fusion of Science and Community**