Possible Lie-admissible covering of the Galilei relativity in Newtonian mechanics for nonconservative and Galilei form-noninvariant systems

Journal Article · Sat Apr 01 04:00:00 EST 1978 · Hadronic J.; (United States)

OSTI ID:6484593

Santill, R M

In order to study the problem of the relativity laws of nonconservative and galilei form-noninvariant systems, two complementary methodological frameworks are presented. The first belongs to the so-called Inverse Problem of Classical Mechanics and consists of the conventional analytic, algebraic and geometrical formulations which underlie the integrability conditions for the existence of a Lagrangian or, independently, of a Hamiltonian. These methods emerge as possessing considerable effectiveness in the identification of the mechanism of Galilei relativity breaking in Newtonian Mechanics by forces not derivable from a potential. For this reason, the second methodological framework is presented. It belongs to the so-called Lie-Admissible Problem in Classical Mechanics and consists of the covering analytic, algebraic and geometrical formulations which are needed for the equations originally conceived by Lagrange and Hamilton. These formulations are characterized by the Lie-admissible algebras which are known to be genuine algebraic covering of Lie algebras, and which in this paper are identified as possessing (a) a direct applicability in Newtonian Mechanics for the case of forces not derivatble from a potential, (b) an analytic origin fully parallel to that of Lie algebras, i.e., via the brackets of the time evolution law, (c) a covering of the conventional canonical formulations as classical realizations, (d) an implementation at a number of levels of Lie's theory, including a fundamental realization as enveloping nonassociative algebras, (e) a generalization of symplectic and contact geometry as geometrical backing and (f) the capability of recovering conventional formulations identically at the limit of null external forces, here interpreted as relativity breaking forces. A covering of the Galilei relativity, called Galilei-admissible relativity, is then conjectured for independent scrutiny.

• Research Organization: Harvard Univ., Cambridge, MA
• OSTI ID: 6484593
• Journal Information: Hadronic J.; (United States), Journal Name: Hadronic J.; (United States) Vol. 1:1; ISSN HAJOD
• Country of Publication: United States
• Language: English

Related Subjects

657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
CLASSICAL MECHANICS
CONSERVATION LAWS
FIELD THEORIES
FUNCTIONS
GALILEI TRANSFORMATIONS
GENERAL RELATIVITY THEORY
GEOMETRY
HAMILTONIANS
LAGRANGIAN FUNCTION
LIE GROUPS
MATHEMATICAL OPERATORS
MATHEMATICS
MECHANICS
QUANTUM OPERATORS
RELATIVITY THEORY
SYMMETRY BREAKING
SYMMETRY GROUPS
TRANSFORMATIONS
VARIATIONAL METHODS