Scaling transformations for the Kepler orbit
Abstract
An analytic method suitable for reducing nonlinear Keplerian motion to linear simple harmonic motion is presented. Scaling transformations are applied to both the state and time variables to reduce the equations of motion into a system of linear constant-coefficient differential equations. The method is demonstrated for examples of Levi-Civita regularization and regularization by Hamiltonian dynamics.
- Publication:
-
NASA STI/Recon Technical Report A
- Pub Date:
- 1980
- Bibcode:
- 1980STIA...8212046P
- Keywords:
-
- Equations Of Motion;
- Kepler Laws;
- Nonlinear Equations;
- Orbit Calculation;
- Scaling;
- Transformations (Mathematics);
- Canonical Forms;
- Cartesian Coordinates;
- Differential Equations;
- Linearization;
- Nonlinear Systems;
- Orbital Mechanics;
- Polar Coordinates;
- Simple Harmonic Motion;
- Astrodynamics