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A completion of A. Bressan's work on axiomatic foundations of the Mach Painlevé type for various classical theories of continuous media. Part 1. Completion of Bressan's work based on the notion of gravitational equivalence of affine inertial frames

Adriano Montanaro (1987)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The work [3], where various classical theories on continuous bodies are axiomatized from the Mach-Painlevè point of view, is completed here in two alternative ways; in that work, among other things, affine inertial frames are defined within classical kinematics. Here, in Part I, a thermodynamic theory of continuous bodies, in which electrostatic phenomena are not excluded, is dealt with. The notion of gravitational equivalence among affine inertial frames and the notion of gravitational isotropy...

A theorem for rigid motions in Post-Newtonian celestial mechanics.

J.M. Gambi, P. Zamorano, P. Romero, M.L. García del Pino (2003)

RACSAM

The velocity field distribution for rigid motions in the Born?s sense applied to Post-Newtonian Relativistic Celestial Mechanics is examined together with its compatibility with the Newtonian distribution.

Hidden symmetries of the gravitational contact structure of the classical phase space of general relativistic test particle

Josef Janyška (2014)

Archivum Mathematicum

The phase space of general relativistic test particle is defined as the 1-jet space of motions. A Lorentzian metric defines the canonical contact structure on the odd-dimensional phase space. In the paper we study infinitesimal symmetries of the gravitational contact phase structure which are not generated by spacetime infinitesimal symmetries, i.e. they are hidden symmetries. We prove that Killing multivector fields admit hidden symmetries of the gravitational contact phase structure and we give...

On the differential equations of the classical and relativistic dynamics for certain generalised Lagrangian functions

Antonio Pignedoli (1987)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

One studies the differential equations of the movement of certain classical and relativistic systems for some special Lagrangian functions. One considers particularly the case in which the problem presents cyclic coordinates. Some electrodynamical applications are studied.

Particles, phases, fields

L. Wojtczak, A. Urbaniak-Kucharczyk, I. Zasada, J. Rutkowski (1996)

Banach Center Publications

The physical properties of particles and phasesare considered in connection with their description by means of the deformation of space-time. The analogy between particle trajectories and phase boundaries is discussed. The geometry and its curvature is related to the Clifford algebraic structure whose construction in terms of the theory of deformation leads to the expected solutions for correlation functions referring to spectroscopy and scattering problems. The stochastic nature of space-time is...

Relations between constants of motion and conserved functions

Josef Janyška (2015)

Archivum Mathematicum

We study relations between functions on the cotangent bundle of a spacetime which are constants of motion for geodesics and functions on the odd-dimensional phase space conserved by the Reeb vector fields of geometrical structures generated by the metric and an electromagnetic field.

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