scholarly journals Brouwer’s satellite solution redux

2021 ◽  
Vol 133 (10) ◽  
Author(s):  
Martin Lara
Keyword(s):  
Hamiltonian Systems ◽  
Artificial Satellite ◽  
Hamiltonian Reduction ◽  
Theoretical Interest ◽  
Keplerian Motion ◽  
New Approach ◽  
Satellite Problem ◽  
Satellite Solution ◽  
Degenerate Hamiltonian Systems ◽  
Single Set

AbstractBrouwer’s solution to the artificial satellite problem is revisited. We show that the complete Hamiltonian reduction is rather achieved in the plain Poincaré’s style, through a single canonical transformation, than using a sequence of partial reductions based on von Zeipel’s alternative for dealing with perturbed degenerate Hamiltonian systems. Beyond the theoretical interest of the new approach as regards the complete reduction of perturbed Keplerian motion, we also show that a solution based on a single set of corrections may yield computational benefits in the implementation of an analytic orbit propagator.

scholarly journals Present problems in relativistic Celestial Mechanics

1986 ◽  
Vol 114 ◽  
pp. 5-17
Author(s):  
V. A. Brumberg
Keyword(s):  
Time Scales ◽  
Celestial Mechanics ◽  
Reference Frames ◽  
Artificial Satellite ◽  
Circular Motion ◽  
Newtonian Approximation ◽  
Satellite Problem ◽  
Solar Perturbations ◽  
Coordinate Functions ◽  
Schwarzschild Problem

Review of the present problems of relativistic celestial mechanics. Advantage is taken of the method suggested earlier by the author and based on using quasi-Galilean coordinates with arbitrary coordinate functions or parameters. As compared with the previous papers the new elements are post-post-Newtonian approximation for the circular motion in the Schwarzschild problem and reduction of the artificial satellite problem including the main solar perturbations to the Schwarzschild problem. Some current questions of time scales definitions, reference frames and reduction of observations are briefly discussed.

scholarly journals Variational Approach to Quasi-Periodic Solution of Nonautonomous Second-Order Hamiltonian Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Juhong Kuang
Keyword(s):  
Periodic Solution ◽  
Variational Methods ◽  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Variational Approach ◽  
Second Order ◽  
New Approach ◽  
Second Order Hamiltonian Systems

We deal with the quasi-periodic solutions of the following second-order Hamiltonian systemsx¨(t)=∇F(t,x(t)), wherex(t)=(x1(t),…,xN(t)), and we present a new approach via variational methods and Minmax method to obtain the existence of quasi-periodic solutions to the above equation.

scholarly journals Topological obstacles to the realizability of integrable Hamiltonian systems by billiards

2019 ◽  
Vol 488 (5) ◽  
pp. 471-475
Author(s):  
V. V. Vedyushkina ◽  
A. T. Fomenko
Keyword(s):  
Magnetic Field ◽  
Hamiltonian Systems ◽  
Degrees Of Freedom ◽  
Integrable Hamiltonian Systems ◽  
Two Degrees Of Freedom ◽  
Degenerate Hamiltonian Systems ◽  
Liouville Equivalence

We introduce the following classes of integrable billiards: elementary billiards, topological, books, with potential, magnetic field, geodesic billiards. These classes are used to test the A.T. Fomenko conjecture about the realizability up to Liouville equivalence by billiards of integrable non-degenerate Hamiltonian systems with two degrees of freedom. In the class of book billiards found topological obstacles to realizability.

New approach to understanding quasiperiodicity in nonintegrable Hamiltonian systems

1985 ◽  
Vol 31 (5) ◽  
pp. 2810-2820 ◽  
Author(s):  
K. Stefański ◽  
H. S. Taylor
Keyword(s):  
Hamiltonian Systems ◽  
New Approach
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