Accession Number : AD0287966

Title :   LORENTZ'S PENDULUM PROBLEM

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : LITTLEWOOD,J.E.

Report Date : SEP 1962

Pagination or Media Count : 1

Abstract : At the Solvay Congress in 1911 Lorentz raised the question: How does a simple pendulum behave when the suspending thread is gradually shortened. This was re evant to the quantum theory of the time. For the equation x + 2 x = O, with subject to natural conditions governing its slow change, it was conjectured that the energy 2x2 + x. 2 is nearly proportional to , or that H( ) = x2 + x.2/ is approximately constant. The paper confirms this, and also the further conjecture that H(oo) - H(-oo) = O-( n) for every n . (Author)

Descriptors :   *DIFFERENTIAL EQUATIONS, *PARTIAL DIFFERENTIAL EQUATIONS, *QUANTUM THEORY, TIME

Distribution Statement : APPROVED FOR PUBLIC RELEASE