Ellipsoidal Full Two Body Problem: An Application to Binary Asteroids
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Ellipsoidal Full Two Body Problem: An Application to Binary Asteroids
Chaotic and resonant Dynamics of full two body problem are investigated through the sphere-ellipsoid and ellipsoid-ellipsoid models. The fourth-order mutual ...
Ellipsoidal Full Two Body Problem: An Application to Binary Asteroids
By
Mahdi Jafari Nadoushan
A Thesis Submitted to the Faculty of Department of Aerospace Engineering Sharif University of Technology In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in Aerospace Engineering
December 2015
Ellipsoidal Full Two Body Problem: An Application to Binary Asteroids Abstract Chaotic and resonant Dynamics of full two body problem are investigated through the sphere-ellipsoid and ellipsoid-ellipsoid models. The fourth-order mutual gravitational potential function is derived in terms of the first-order moment of inertia for both models. Employing Hamiltonian formulation and elliptical expansion, the resonant angles appear in the equations which include secondary’s attitude and mean anomaly for sphere-ellipsoid model and attitude of both bodies and mean anomaly for ellipsoid-ellipsoid model. In first step, resonances overlapping criteria is applied to the first-order resonances of sphereellipsoid model and the effect of the asphericity and orbital eccentricity on the onset of chaos is studied. By adding second-order resonances, the criteria is modified and also some new parameters emerge which affect the onset of chaos and occurrence Chirikov diffusion. In the second step, using ellipsoid -ellipsoid model, the local stability of relative equilibria is analyzed and a method for exploration of geographic information of resonances is purposed. Occurrence of Chirikov diffusion in the rotation of both bodies is also investigated according to the geographic information, physical, and orbital parameters. The results show that the Chirikov diffusion and therefore simultaneously chaos is occurred when both masses and their distribution are of the same order, which is rare in the binary asteroids populations.
Keywords: Full Two Body Problem, Binary Asteroids, Hamiltonian Dynamics, Spin-SpinOrbit Resonance, Diffusion Chirikov, Simultaneously Chaos
