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} }
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.
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References
SHOWING 1-10 OF 13 REFERENCES
A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: INDEX OF TERMS EMPLOYED
- Geology
- 1988
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
A treatise on the analytical dynamics of particles and rigid bodies, 4th ed
- Universidad de Salamanca, Departamento de Matemáticas, Plaza de la Merced
- 1947
Die Principe der Dynamik, Handsbuch der Physik
- Die Principe der Dynamik, Handsbuch der Physik
- 1927