Other
Scientific paper
Apr 1983
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983jgcd....6..124b&link_type=abstract
Journal of Guidance, Control and Dynamics, vol. 6, Mar.-Apr. 1983, p. 124-128.
Other
Astronomical Coordinates, Gravitational Effects, Three Body Problem, Angular Velocity, Degrees Of Freedom, Distance, Euler-Lagrange Equation, Orthogonal Functions, Time Functions
Scientific paper
A symmetrical system of distance coordinates is used to give the details of a complete numerical solution of the gravitation problem, including the three angular degrees of freedom. The three coordinate axes pass through the masses with the positive halves intersecting at angles of 120 deg with each other at a moving origin. The distance cordinates are taken as the signed distances of the masses from the moving origin. If the angular orientation of the coordinate axes is defined by the Euler angles, an attempt to determine these angles by integrating their time rates of change fails because of singularities. It is shown that such singularities are avoided by the use of Rodrigues' orthogonal matrix to specify the angular orientation. The Lagrange equations are solved for the appropriate time derivatives, separating the distance variables from themselves and the angular velocities, thus making possible a simple computer numerical solution.
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