Time transformations in the extended phase-space

Details Time transformations in the extended phase-space Time transformations in the extended phase-space

Jun 1975

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975cemec..11..469z&link_type=abstract

Celestial Mechanics, vol. 11, June 1975, p. 469-482. NSF-supported research.

Mathematics

10

Celestial Mechanics, Equations Of Motion, Time Dependence, Transformations (Mathematics), Two Body Problem, Euler-Lagrange Equation, Numerical Stability, Partial Differential Equations, Phase-Space Integral

Scientific paper

Time transformations that depend on all generalized variables in the phase-space (i.e., on the momenta and on the coordinates) are studied with a view toward the stabilization and regularization of the equations of motion. Sundman's (1912) classical transformation of the time to a new independent variable (involving the distance between two bodies participating in a close approach or collision), formerly generalized by using the potential function to transform the time, is further generalized by using the Lagrangian function for the same purpose. In this approach, the transformation by the potential appears as a special case. An integrable (explicit) relation is shown to exist between the new and original time-variables. The new independent variable is shown to constitute the line-element of the geodesics.

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