On a Possible Lie Admissible Covering of the Galilei Relativity in Newtonian Mechanics for Nonconservative and Galilei Form - Noninvariant Systems
On a Possible Lie Admissible Covering of the Galilei Relativity in Newtonian Mechanics for Nonconservative and Galilei Form - Noninvariant Systems
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发表时间：
1978-04
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通讯作者：
R. Santilli
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作者：
R. Santilli
为了研究非保守系统和伽利雷形式非不变系统的相对性问题，提出了两种互补的方法框架。第一个问题属于所谓的经典力学逆问题，由传统的解析、代数和几何公式组成，这些公式是拉格朗日量或哈密顿量存在的可积性条件的基础。这些方法在确定牛顿力学中伽利略相对论因不可由势导出的力而断裂的机理方面具有相当大的有效性。基于这个原因，本文提出了第二个方法框架。它属于经典力学中所谓的李可容许问题，由拉格朗日和汉密尔顿最初设想的方程所需要的解析式、代数式和几何式组成。这些公式的特征是李可容许代数，它们被认为是李代数的真正代数覆盖，并且在本文中被认为具有(a)在牛顿力学中对于不能由势推导出的力的情况的直接适用性，(b)解析原点与李代数的解析原点完全平行，即通过时间演化律的括号，(c)作为经典实现的常规正则表达式的覆盖。(d)李氏理论在多个层面上的实现，包括包膜非结合代数的基本实现，(e)作为几何背景的辛几何和接触几何的推广，以及(f)在零外力的极限下完全恢复常规公式的能力，这里解释为相对论破断力。伽利略相对论的一个覆盖，称为伽利略可接受相对论，然后被推测为独立的审查。«少
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 formulationsmore » 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.« less