Addendum to: on a possible Lie-admissible covering of the Galilei relativity in Newtonian mechanics for nonconservative and Galilei form-noninvariant systems

Journal Article · Sun Oct 01 04:00:00 EDT 1978 · Hadronic J.; (United States)

OSTI ID:6444259

Santilli, R M

In this note I first present a needed clarification on the realization of Lie-admissible algebras for non-conservative Newtonian systems considerd in a recent paper. The following aspects are then treated (A) I introduce a new realization which is directly applicable to all nonconservative systems of the admitted class (local, class C and regular) via the solution of simple algebraic systems. (B) I indicated that such a realization yields compatible generalized formulations of Hamilton-admissible, Lie-admissible and symplectic-admissible type. (C) I show in details that such a realization is applicable to the construction of th eLie-admissible generalization of the Galilei relativity I proposed for nonconservative systems, and I work out a number of examples. (D) I then prove that, for the subclass of autonomous systems, the time-component of the proposesd generalized relativity is indeed universal, that is, it provides the form-invariant description of all systems considered, while being able to recover the conventional time component of the Galilei relativity at the limit of the null value of the Galilei symmetry-breaking forces. And, finally, (E) I prove that the dual Lie-admissible algebraic and sympletic-admissible geometrical character of the proposed generalized relativity is independent from the selected system of local coordinates, by therefore confirming the hope for a coordinate free-globalization of the symplectic-admissible geometry and relativity.

• Research Organization: Harvard Univ., Cambridge, MA
• OSTI ID: 6444259
• Journal Information: Hadronic J.; (United States), Journal Name: Hadronic J.; (United States) Vol. 1:4; ISSN HAJOD
• Country of Publication: United States
• Language: English

Related Subjects

658000* -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CLASSICAL MECHANICS
FIELD THEORIES
FUNCTIONS
GALILEI TRANSFORMATIONS
GENERAL RELATIVITY THEORY
GEOMETRY
GLOBAL ANALYSIS
LAGRANGIAN FUNCTION
LIE GROUPS
MATHEMATICS
MECHANICS
RELATIVITY THEORY
SYMMETRY BREAKING
SYMMETRY GROUPS
TIME DEPENDENCE
TRANSFORMATIONS