The structure of time and inertial forces in Lagrangian mechanics

@article{Diaz2008TheSO,
  title={The structure of time and inertial forces in Lagrangian mechanics},
  author={J. Munoz D'iaz},
  journal={arXiv: Mathematical Physics},
  year={2008}
}
  • J. D'iaz
  • Published 27 January 2008
  • Physics
  • arXiv: Mathematical Physics
Classically time is kept fixed for infinitesimal variations in problems in mechanics. Apparently, there appears to be no mathematical justification in the literature for this standard procedure. This can be explained canonically by unveiling the intrinsic mathematical structure of time in Lagrangian mechanics. Moreover, this structure also offers a general method to deal with inertial forces. 
Relativistic forces in Lagangian mechanics
We give a general definition of \emph{relativistic force} in the context of Lagrangian mechanics. Once this is done we prove that the only relativistic forces which are linear on the velocities are
A mathematical objection to the existence of relativistic mechanical systems of several particles
We will prove that, in general, a system formed by several particles moving along relativistic trajectories can not be described by a mechanical system. The contradiction that leads to the previous
Flux-variational formulation of relativistic perfect fluids
Newton's Second Law in Field Theory
Klein-Gordon equation from Maxwell-Lorentz dynamics
We consider Maxwell-Lorentz dynamics: that is to say, Newton's law under the action of a Lorentz's force which obeys the Maxwell equations. A natural class of solutions are those given by the
A note on the quantization of tensor fields and quantization of mechanical systems
In the present work we present a canonical method of quantization for contravariant tensor fields. Its natural application to quantizing classical mechanical systems is proved to coincide with that
Time in classical and quantum mechanics
In this article we study the nature of time in Mechanics. The fundamental principle, according to which a mechanical system evolves governed by a second order differential equation, implies the
On the quantization of mechanical systems
We present a canonical way of assigning to each magnitude of a classical mechanical system a differential operator in the configuration space, thus rigorously establishing the Correspondence
On the foundation of Mechanics
This note is an extended version of "A note on the foundations of Mechanics", arXiv: 1404.1321 [math-ph]. A presentation of its contents was given in a talk in memorial homage to the professor Juan
...
...

References

SHOWING 1-10 OF 13 REFERENCES
A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: INDEX OF TERMS EMPLOYED
TLDR
The Sciencemadness library currently holds 50426 pages of reading and reference material in 107 volumes, including algebraic geometry, which is the foundation of most modern fields of geometry, including mathematics, physics, and astronomy.
VorlesungenVorlesungen¨Vorlesungenüber Theoretische Physik
  • VorlesungenVorlesungen¨Vorlesungenüber Theoretische Physik
  • 1949
Die allgemeinen Integrationsmethoden der analytischen Mechanik
Mécanique analytique et théorie des quanta
Die Principe der Dynamik, Handsbuch der Physik
  • Die Principe der Dynamik, Handsbuch der Physik
  • 1927
...
...