The Maupertuis principle and geodesic flows on the sphere arising from integrable cases in the dynamics of a rigid body

Abstract

We construct a kink solution on a non-BPS D-brane using Berkovits' formulation of superstring field theory in the level truncation scheme. The tension of the kink reproduces 95% of the expected BPS D-brane tension. We also find a lump-like solution which is interpreted as a kink-antikink pair, and investigate some of its properties. These results may be considered as successful tests of Berkovits' superstring field theory combined with the modified level truncation scheme.

The Maupertuis Principle and Canonical Transformations of the Extended Phase Space

“…The Maupertuis transformation maps any integrable system with a natural Hamilton function H(p, q) into the other integrable system on the same phase space M. Namely this property has been used for the search of the new integrable systems (see references within [19,10,5,27,28]). The Maupertuis principle for integrable systems with a nonnatural Hamilton function is discussed in [22].…”

“…which relates the initial hamiltonian vector field ξ on M with the other hamiltonian vector field ξ defined on the same phase space M [5].…”

“…The modern interpretation of the Maupertuis' principle may be found in [2,22,5]. The reduced action S 0 = p dq is independent of any evolution parameter.…”

Bäcklund transformations for the nonholonomic Veselova system

“…of the Casimir functions one gets symplectic leaf of e * (3) which is a four-dimensional symplectic manifold equivalent to T * S 2 [3]. Let us rewrite Hamiltonians (3.5-3.6) and (3.9-3.10) in term of redundand variables (x, p) and (x, J) on T * R 3 .…”

“…If the integral of the system is polynomial in momenta, the integrals of the geodesic flows are also polynomial of the same degree. There are a few examples of integrable geodesic flows on the sphere S 2 whose integrals are polynomials in momenta of degree four, see [3,4,21,37,40] and references within.…”