The geometrization of Galilei’s principle. (English) Zbl 0637.58003
The author presents a sequence of reformulations and generalizations of the classical Galilei’s principle. They include the motion of mechanical systems on manifolds (non-linear configuration spaces), of relativistic systems, motion in gauge fields, etc. The language of connections, geodesics, symplectic structures and some other geometrical objects is used.
Reviewer: Yu.E.Gliklikh
MSC:
37J99 | Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems |
58E30 | Variational principles in infinite-dimensional spaces |
70F99 | Dynamics of a system of particles, including celestial mechanics |
83C10 | Equations of motion in general relativity and gravitational theory |