Figure 5 - uploaded by Javier Roa
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Schwarzschild geodesic (solid line) compared to generalized cardioids and generalized sinusoidal spirals (dashed line).
Source publication
The invariance of the Lagrangian under time translations and rotations in Kepler's problem yields the conservation laws related to the energy and angular momentum. Noether's theorem reveals that these same symmetries furnish generalized forms of the first integrals in a special nonconservative case, which approximates various physical models. The s...
Citations
New solutions to the central force problem are detailed. These solutions correspond to a class of curves which is obtained by the generalization of a geometric property of conics. This class contains a wide variety of well-known curves and in particular admits the logarithmic spiral as a limiting case. The determination of the law of central force is made by using Siacci’s theorem. This law allows us to link in a single relation the linear, inverse square and inverse cubic forces. New trajectories and corresponding analytic solutions are provided. The results are relevant to the fields of celestial mechanics and orbital dynamics.
