# Gauge Freedom in Orbital Mechanics

@article{Efroimsky2005GaugeFI, title={Gauge Freedom in Orbital Mechanics}, author={Michael Efroimsky}, journal={Annals of the New York Academy of Sciences}, year={2005}, volume={1065} }

Abstract: Both orbital and attitude dynamics employ the method of variation of parameters. In a non‐perturbed setting, the coordinates (or the Euler angles) are expressed as functions of the time and six adjustable constants called elements. Under disturbance, each such expression becomes ansatz, the “constants” being endowed with time dependence. The perturbed velocity (linear or angular) consists of a partial time derivative and a convective term containing time derivatives of the “constants…

## 32 Citations

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Construction of an accurate theory of orbits about a precessing and nutating oblate planet, in terms of osculating elements defined in a frame associated with the equator of date, was started in…

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## References

SHOWING 1-10 OF 26 REFERENCES

### The method of variation of constants and multiple time scales in orbital mechanics.

- PhysicsChaos
- 2003

It is shown that constraints in the method of variation of constants can be generalized in analogy to gauge theories in physics, and that different constraints can offer conceptual advances and methodological benefits to the solution of the underlying problem.

### Gauge symmetry of the N-body problem in the Hamilton–Jacobi approach

- Physics
- 2003

In most books the Delaunay and Lagrange equations for the orbital elements are derived by the Hamilton–Jacobi method: one begins with the two-body Hamilton equations in spherical coordinates,…

### Equations for the orbital elements: Hidden Symmetry

- Physics
- 2002

We revisit the Lagrange and Delaunay systems of equations for the orbital elements, and point out a previously neglected aspect of these equations: in both cases the orbit resides on a certain…

### Implicit gauge symmetry emerging in the N-body problem of celestial mechanics

- Physics
- 2002

We revisit the Lagrange and Delaunay systems of equations for the orbital elements, and point out a previously neglected aspect of these equations: in both cases the orbit resides on a certain…

### Gauge freedom in the N-body problem of celestial mechanics

- Physics
- 2004

The goal of this paper is to demonstrate how the internal symmetry of the N-body celestial-mechanics problem can be exploited in orbit calculation.
We start with summarising research reported in…

### Analysis of J2-perturbed motion using mean non-osculating orbital elements

- Physics
- 2004

This paper investigates the long-period and secular dynamics of a satellite about an oblate primary while relieving the assumption that the perturbed orbit is instantaneously parameterized by…

### Elements of spin motion

- Physics
- 1994

For use in numerical studies of rotational motion, a set of elements is introduced for the torque-free rotational motion of a rigid body around its barycenter. The elements are defined as the initial…

### Mitigating the integration error in numerical simulations of Newtonian systems

- Computer Science
- 2006

It is shown that by choosing an appropriate gauge function the numerical integration error dramatically decreases and one can achieve much better accuracy compared to the standard state variables for a given time‐step.

### Analytical methods for the orbits of artificial satellites of the Moon

- Physics
- 1971

The motion of a close artificial satellite of the Moon is considered. The principal perturbations taken into account are caused by the nonsphericity of the Moon and the attraction of the Earth and…

### Long-Term Evolution of Orbits About A Precessing Oblate Planet: 1. The Case of Uniform Precession

- Physics, Geology
- 2005

It was believed until very recently that a near-equatorial satellite would always keep up with the planet’s equator (with oscillations in inclination, but without a secular drift). As explained in…