Abstract
This chapter derives the general equations for interacting rigid bodies accounting for their rolling motion on each other. The derivation of the non-rolling motions has been given previously, but to accommodating rolling and slipping motion it is necessary to develop a non-holonomic form of the equations of motion. The resulting derivation shows that the key analysis parameters for a collection of grains that gravitationally attract and rest on each other are preserved in this more advanced formulation. The chapter ends with a simple application of these results to a series of bodies that can roll on each other, satisfying a non-holonomic constraint.
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References
Cendra, H., Marsden, J.E.: Geometric mechanics and the dynamics of asteroid pairs. Dyn. Syst. Int. J. 20, 3–21 (2005)
Fujiwara, A., Kawaguchi, J., Yeomans, D.K., Abe, M., Mukai, T., Okada, T., Saito, J., Yano, H., Yoshikawa, M., Scheeres, D.J., et al.: The rubble-pile asteroid Itokawa as observed by Hayabusa. Science 312(5778), 1330–1334 (2006)
Greenwood, D.T.: Classical Dynamics. Dover, Mineola (1997)
Holsapple, K.A.: On YORP-induced spin deformations of asteroids. Icarus 205(2), 430–442 (2010)
Liebenthal, E.: Untersuchungen uber die Attraction zweier homogener Korper. PhD thesis, Universitat Greifswald (1880)
Moeckel, R.: On central configurations. Math. Z. 205(1), 499–517 (1990)
Pravec, P., Harris, A.W.: Fast and slow rotation of asteroids. Icarus 148, 12–20 (2000)
Sánchez, P., Scheeres, D.J.: Simulating asteroid rubble piles with a self-gravitating soft-sphere distinct element method model. Astrophys. J. 727, 120 (2011)
Scheeres, D.J.: Stability in the full two-body problem. Celest. Mech. Dyn. Astron. 83(1), 155–169 (2002)
Scheeres, D.J.: Relative equilibria for general gravity fields in the sphere-restricted full 2-body problem. Celest. Mech. Dyn. Astron. 94, 317–349 (2006)
Scheeres, D.J.: Minimum energy configurations in the N-body problem and the celestial mechanics of granular systems. Celest. Mech. Dyn. Astron. 113(3), 291–320 (2012)
Scheeres, D.J.: Relative equilibria in the full N-body problem with applications to the equal mass problem. In: Recent Advances in Celestial and Space Mechanics, pp. 31–81. Springer, Cham (2016)
Scheeres, D.J.: Correction to: stability of the Euler resting N-body relative equilibria. Celest. Mech. Dyn. Astron. 130, 55–56 (2018)
Scheeres, D.J.: Stability of the Euler resting N-body relative equilibria. Celest. Mech. Dyn. Astron. 130(3), 26 (2018)
Simo, J.C., Lewis, D., Marsden, J.E.: Stability of relative equilibria. Part I: the reduced energy-momentum method. Arch. Ration. Mech. Anal. 115(1), 15–59 (1991)
Walsh, K.J., Richardson, D.C., Michel, P.: Spin-up of rubble-pile asteroids: disruption, satellite formation, and equilibrium shapes. Icarus 220(2), 514–529 (2012)
Werner, R.A., Scheeres, D.J.: Mutual potential of homogeneous polyhedra. Celest. Mech. Dyn. Astron. 91, 337–349 (2005)
Acknowledgements
This chapter was derived from a set of lectures given at the SDSM 2017 School entitled: “Satellite Dynamics and Space Missions: Theory and Applications of Celestial Mechanics,” held August 28–September 2, 2017, in San Martino al Cimino (VT), Italy. The author acknowledges support from NASA’s SSERVI program (Institute for the Science of Exploration Targets) through institute grant number NNA14AB03A. The author acknowledges Dr. Giulio Baù for his insightful and comprehensive review of this contribution, which greatly helped to improve its discussion and correctness.
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Scheeres, D.J. (2019). Celestial Mechanics of Rubble Pile Bodies. In: Baù, G., Celletti, A., Galeș, C., Gronchi, G. (eds) Satellite Dynamics and Space Missions. Springer INdAM Series, vol 34. Springer, Cham. https://doi.org/10.1007/978-3-030-20633-8_5
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DOI: https://doi.org/10.1007/978-3-030-20633-8_5
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