History of rediscovery

The LRL vector A is a constant of motion of the important Kepler problem, and is useful in describing astronomical orbits, such as the motion of the planets. Nevertheless, it has never been well known among physicists, possibly because it is less intuitive than momentum and angular momentum. Consequently, it has been rediscovered independently several times over the last three centuries.[7] Jakob Hermann was the first to show that A is conserved for a special case of the inverse-square central force,[11] and worked out its connection to the eccentricity of the orbital ellipse. Hermann's work was generalized to its modern form by Johann Bernoulli in 1710.[12] At the end of the century, Pierre-Simon de Laplace rediscovered the conservation of A, deriving it analytically, rather than geometrically.[13] In the middle of the nineteenth century, William Rowan Hamilton derived the equivalent eccentricity vector defined below,[8] using it to show that the momentum vector p moves on a circle for motion under an inverse-square central force (Figure 3).[6] At the beginning of the twentieth century, Josiah Willard Gibbs derived the same vector by vector analysis.[14] Gibbs' derivation was used as an example by Carle Runge in a popular German textbook on vectors,[15] which was referenced by Wilhelm Lenz in his paper on the (old) quantum mechanical treatment of the hydrogen atom.[16] In 1926, the vector was used by Wolfgang Pauli to derive the spectrum of hydrogen using modern quantum mechanics, but not the Schrödinger equation;[3] after Pauli's publication, it became known mainly as the Runge–Lenz vector.

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