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FIZIKA A 19 (2010) 4 , 197-214
 
EULER-LAGRANGE SOLUTION FOR CALCULATING PARTICLE ORBITS IN GRAVITATIONAL FIELDS
A. SFARTI
387 Soda Hall, UC Berkeley, Berkeley, U. S. A.
Received 4 November 2010; Accepted 19 January 2011
Online 15 April 2011
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.
PACS numbers: 03.30.+p, 52.20.Dq, 52.70.Nc
UDC 531.18, 521.92
Keywords: general relativity, Schwarzschild metric,
Reissner-Nordström metric, advancement of perihelion, Euler-Lagrange formalism
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