Note on the representation of many-particle dynamics as higher-order single-particle dynamics, with a means to relativistic elevation of Newtonian dynamics.

Details Note on the representation of many-particle dynamics as higher-order single-particle dynamics, with a means to relativistic elevation of Newtonian dynamics. Note on the representation of many-particle dynamics as higher-order single-particle dynamics, with a means to relativistic elevation of Newtonian dynamics.

May 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992jmp....33.1675k&link_type=abstract

Journal of Mathematical Physics, Vol. 33, No. 5, p. 1675 - 1684

Mathematics

Mathematical Physics

5

Scientific paper

It is shown how (first in Newtonian physics), by processes of repeated differentiation of equations of motion and of algebraic elimination, the dynamics of many particles may be brought to another equivalent representation, that of a single higher-order equation of motion for a single particle. Here a higher-order Lagrangian followed by an Ostrogradsky Hamiltonian may be brought into play. The higher-order one-particle representation translates simply and directly (but not uniquely) into relativistic generalization (because only a single world line is being described), in which the Poincaré group is canonically represented in an Ostrogradsky Hamiltonian formulation. The examples of the Kepler problem and the harmonic oscillator are elaborated in detail.

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