Non-relativistic
mechanics (

**FMP-7**) as like as classical field theory (**FMP-3**) is adequately formulated in the terms of fiber bundles**over the time axis***Q->R***and jet manifolds of their sections.***R*
If a configuration
space

**of a mechanical system has no preferable fibration***Q***, we obtain a general formulation of relativistic mechanics, including Special Relativity on the Minkowski space***Q->R***. This fomulation involves a more sophisticated technique of jets of one-dimensional submanifolds. In the framework of this formalism, submanifolds of a manifold***Q=R^4***are identified if they are tangent to each other at points of***Q***with some order. Jets of sections are particular jets of submanifolds when***Q***is a fiber bundle and these submanifolds are its sections. In contrast with jets of sections, jets of submanifolds in relativistic mechanics admit arbitrary transformations of time***Q->R***including the Lorentz transformations, but not only***t’= t(q)***. in the non-relativistic case.***t’=t+const*
Note that jets
of two-dimensional submanifolds provide a formulation of classical string
theory.

A velocity
space of relativistic mechanics is the first-order jet manifold

**of one-dimensional submanifolds of the configuration space***J^1Q***. The jet bundle***Q***is projective, and one can think of its fibers as being spaces of the three velocities of a relativistic system. The four velocities of a relativistic system are represented by elements of the tangent bundle***J^1Q → Q***of a configuration space***TQ***. Lagrangian formalism of relativistic mechanics on the jet bundle***Q***is developed.***J^1Q → Q***References**:

G.
Giachetta, L. Mangiarotti, G. Sardanashvily, Geometric Formulation of Classical
and Quantum Mechanics (World Scientific, 2010)

G.
Sardanashvily, Relativistic
mechanics in a general setting,

*Int. J. Geom. Methods Mod. Phys.***7**(2010) 1307-1319**WikipediA**: Relativistic system (mathematics)

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