Classical Physics

    

Vector Kinematic Analysis of Keplerian Velocity from Hamilton’s Hodograph

Authors: Herve Le Cornec

Many authors in the literature focused on Hamilton's hodograph of the Keplerian motion but none of them developed a vector kinematic analysis of the peculiar velocity shown by the hodograph, so we perform it here. As expected, the analysis predicts Kepler's laws and the mathematical structure of Newton's acceleration. It also leads to new expressions for the eccentricity and the classical mechanical energy. We then discuss the relationship between the geometric acceleration given by Hamilton's kinematics and the physical one stated by Newton.

Comments: 3 Pages.

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Submission history

[v1] 2025-07-28 08:52:11
[v2] 2025-08-02 17:44:20
[v3] 2025-08-27 10:26:27

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