000			02489pam a2200253 a 4500
005			20171214154744.0
008			821022s1983 nyu b 001 0 eng
020			_a0387094822
040			_cIITK
041			_aeng
082	0	0	_a531 _bSa59f v.2
100	1		_aSantilli, Ruggero Maria
245	1	0	_aFoundations of theoretical mechanics II _cSantilli, Ruggero Maria _bbirkhoffian generalization of Hamiltonian mechanics
260			_aNew York _bSpringer-Verlag _c1983
300			_axviii, 370p
440		0	_aTexts and monographs in physics
490			_aBeiglbock, W. (ed.) _aLieb, E. H. (ed.) _aRegge, T. (ed.) _aThirring, W. (ed.)
505			_aIn the preceding volume,l I identified necessary and sufficient conditions for the existence of a representation of given Newtonian systems via a variational principle, the so-called conditions of variational self-adjointness. A primary objective of this volume is to establish that all Newtonian systems satisfying certain locality, regularity, and smoothness conditions, whether conservative or nonconservative, can be treated via conventional variational principles, Lie algebra techniques, and symplectic geometrical formulations. This volume therefore resolves a controversy on the repre­ sentational capabilities of conventional variational principles that has been 2 lingering in the literature for over a century, as reported in Chart 1. 3. 1. The primary results of this volume are the following. In Chapter 4,3 I prove a Theorem of Direct Universality of the Inverse Problem. It establishes the existence, via a variational principle, of a representation for all Newtonian systems of the class admitted (universality) in the coordinates and time variables of the experimenter (direct universality). The underlying analytic equations turn out to be a generalization of conventional Hamilton equations (those without external terms) which: (a) admit the most general possible action functional for first-order systems; (b) possess a Lie algebra structure in the most general possible, regular realization of the product; and (c) 1 Santilli (1978a). As was the case for Volume I, the references are listed at the end of this volume, first in chronological order and then in alphabetic order.
650		0	_aMechanics
650		0	_aInverse problems (Differential equations)
650		0	_aHamiltonian systems
700			_aBeiglbock, W. (ed.) _aLieb, E. H. (ed.) _aRegge, T. (ed.) _aThirring, W. (ed.)
942			_cBK
999			_c557317 _d557317