Izvorni znanstveni članak
Euler-Lagrange solution for calculating particle orbits in gravitational fields
A. Sfarti
; 387 Soda Hall, UC Berkeley, Berkeley, U. S. A.
Sažetak
The derivation of particle equations of motion in gravitational fields in general relativity is done routinely via the use of covariant derivatives. Since the geodesic equations based on covariant derivatives are derived from the Euler-Lagrange equations in the first place, and since the Euler-Lagrange formalism is very intuitive, easy to derive with no mistakes, there is every reason to use them even for the most complicated situations. In the current paper we show the application of the lagrangian equations for various scenarios in general relativity. A special paragraph is dedicated to the radial motion. In textbooks, radial motion is given less attention than orbital motion, perhaps because solving the equations of motion is more difficult than in the case of orbital motion.
Ključne riječi
general relativity; Schwarzschild metric; Reissner-Nordström metric; advancement of perihelion; Euler-Lagrange formalism
Hrčak ID:
302802
URI
Datum izdavanja:
1.9.2010.
Posjeta: 174 *