2 research outputs found
Duality properties of Gorringe-Leach equations
In the category of motions preserving the angular momentum's direction,
Gorringe and Leach exhibited two classes of differential equations having
elliptical orbits. After enlarging slightly these classes, we show that they
are related by a duality correspondence of the Arnold-Vassiliev type. The
specific associated conserved quantities (Laplace-Runge-Lenz vector and
Fradkin-Jauch-Hill tensor) are then dual reflections one of the othe
Not so Classical Mechanics - Unexpected Symmetries of Classical Motion
A survey of topics of recent interest in Hamiltonian and Lagrangian dynamical
systems, including accessible discussions of regularization of the central
force problem; inequivalent Lagrangians and Hamiltonians; constants of central
force motion; a general discussion of higher-order Lagrangians and Hamiltonians
with examples from Bohmian quantum mechanics, the Korteweg-de Vries equation
and the logistic equation; gauge theories of Newtonian mechanics; classical
spin, Grassmann numbers, and pseudomechanics.Comment: Einstein Centennial Review Article, 48 page